VAE.ipynb

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  "metadata": {
    "colab": {
      "provenance": [],
      "toc_visible": true,
      "gpuType": "T4",
      "authorship_tag": "ABX9TyNclOcvOjHFla2n87BQkwqZ",
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    },
    "accelerator": "GPU"
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/weedge/doraemon-nb/blob/main/VAE.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Implementation of Variational AutoEncoder (VAE)\n",
        "\n",
        "https://ar5iv.labs.arxiv.org/html/1312.6114\n"
      ],
      "metadata": {
        "id": "-tmg90PXwsXR"
      }
    },
    {
      "cell_type": "code",
      "execution_count": 1,
      "metadata": {
        "id": "IeKdLGmej02x"
      },
      "outputs": [],
      "source": [
        "import torch\n",
        "import torch.nn as nn\n",
        "\n",
        "import numpy as np\n",
        "\n",
        "from tqdm import tqdm\n",
        "from torchvision.utils import save_image, make_grid\n",
        "\n",
        "DEVICE = \"cuda\" if torch.cuda.is_available() else \"cpu\"\n"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "# 1. Load Dataset\n"
      ],
      "metadata": {
        "id": "6LmcZdq9w9kD"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "from torchvision.datasets import MNIST\n",
        "import torchvision.transforms as transforms\n",
        "from torch.utils.data import DataLoader\n",
        "\n",
        "batch_size = 100\n",
        "dataset_path = '~/datasets'\n",
        "\n",
        "mnist_transform = transforms.Compose([\n",
        "        transforms.ToTensor(),\n",
        "])\n",
        "\n",
        "kwargs = {'num_workers': 1, 'pin_memory': True}\n",
        "\n",
        "train_dataset = MNIST(dataset_path, transform=mnist_transform, train=True, download=True)\n",
        "test_dataset  = MNIST(dataset_path, transform=mnist_transform, train=False, download=True)\n",
        "\n",
        "train_loader = DataLoader(dataset=train_dataset, batch_size=batch_size, shuffle=True, **kwargs)\n",
        "test_loader  = DataLoader(dataset=test_dataset,  batch_size=batch_size, shuffle=False, **kwargs)\n"
      ],
      "metadata": {
        "id": "bQl_oOwLw80z"
      },
      "execution_count": 2,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "# 2. Define our model: Variational AutoEncoder (VAE)\n"
      ],
      "metadata": {
        "id": "vqOWO4EwxR0s"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "\"\"\"\n",
        "    A simple implementation of Gaussian MLP Encoder and Decoder\n",
        "\"\"\"\n",
        "\n",
        "class Encoder(nn.Module):\n",
        "\n",
        "    def __init__(self, input_dim, hidden_dim, latent_dim):\n",
        "        super(Encoder, self).__init__()\n",
        "\n",
        "        self.FC_input = nn.Linear(input_dim, hidden_dim)\n",
        "        self.FC_input2 = nn.Linear(hidden_dim, hidden_dim)\n",
        "        self.FC_mean  = nn.Linear(hidden_dim, latent_dim)\n",
        "        self.FC_var   = nn.Linear (hidden_dim, latent_dim)\n",
        "\n",
        "        self.LeakyReLU = nn.LeakyReLU(0.2)\n",
        "\n",
        "        self.training = True\n",
        "\n",
        "    def forward(self, x):\n",
        "        h_       = self.LeakyReLU(self.FC_input(x))\n",
        "        h_       = self.LeakyReLU(self.FC_input2(h_))\n",
        "        mean     = self.FC_mean(h_)\n",
        "        log_var  = self.FC_var(h_)                     # encoder produces mean and log of variance\n",
        "                                                       #             (i.e., parateters of simple tractable normal distribution \"q\"\n",
        "\n",
        "        return mean, log_var\n"
      ],
      "metadata": {
        "id": "bndfcenUxRhw"
      },
      "execution_count": 3,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "class Decoder(nn.Module):\n",
        "    def __init__(self, latent_dim, hidden_dim, output_dim):\n",
        "        super(Decoder, self).__init__()\n",
        "        self.FC_hidden = nn.Linear(latent_dim, hidden_dim)\n",
        "        self.FC_hidden2 = nn.Linear(hidden_dim, hidden_dim)\n",
        "        self.FC_output = nn.Linear(hidden_dim, output_dim)\n",
        "\n",
        "        self.LeakyReLU = nn.LeakyReLU(0.2)\n",
        "\n",
        "    def forward(self, x):\n",
        "        h     = self.LeakyReLU(self.FC_hidden(x))\n",
        "        h     = self.LeakyReLU(self.FC_hidden2(h))\n",
        "\n",
        "        x_hat = torch.sigmoid(self.FC_output(h))\n",
        "        return x_hat\n"
      ],
      "metadata": {
        "id": "FHNHC0uixXpI"
      },
      "execution_count": 4,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "class Model(nn.Module):\n",
        "    def __init__(self, Encoder, Decoder):\n",
        "        super(Model, self).__init__()\n",
        "        self.Encoder = Encoder\n",
        "        self.Decoder = Decoder\n",
        "\n",
        "    def reparameterization(self, mean, var):\n",
        "        epsilon = torch.randn_like(var).to(DEVICE)        # sampling epsilon\n",
        "        z = mean + var*epsilon                          # reparameterization trick\n",
        "        return z\n",
        "\n",
        "\n",
        "    def forward(self, x):\n",
        "        mean, log_var = self.Encoder(x)\n",
        "        z = self.reparameterization(mean, torch.exp(0.5 * log_var)) # takes exponential function (log var -> var)\n",
        "        x_hat            = self.Decoder(z)\n",
        "\n",
        "        return x_hat, mean, log_var\n"
      ],
      "metadata": {
        "id": "dcdYgKB7xaCb"
      },
      "execution_count": 5,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# Model Hyperparameters\n",
        "x_dim  = 784\n",
        "hidden_dim = 400\n",
        "latent_dim = 200\n",
        "\n",
        "encoder = Encoder(input_dim=x_dim, hidden_dim=hidden_dim, latent_dim=latent_dim)\n",
        "decoder = Decoder(latent_dim=latent_dim, hidden_dim = hidden_dim, output_dim = x_dim)\n",
        "\n",
        "model = Model(Encoder=encoder, Decoder=decoder).to(DEVICE)\n",
        "print(model)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "8vnLzLjnxdtZ",
        "outputId": "a4981dfe-e411-4b8a-e27b-13130d7d8ef6"
      },
      "execution_count": 6,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model(\n",
            "  (Encoder): Encoder(\n",
            "    (FC_input): Linear(in_features=784, out_features=400, bias=True)\n",
            "    (FC_input2): Linear(in_features=400, out_features=400, bias=True)\n",
            "    (FC_mean): Linear(in_features=400, out_features=200, bias=True)\n",
            "    (FC_var): Linear(in_features=400, out_features=200, bias=True)\n",
            "    (LeakyReLU): LeakyReLU(negative_slope=0.2)\n",
            "  )\n",
            "  (Decoder): Decoder(\n",
            "    (FC_hidden): Linear(in_features=200, out_features=400, bias=True)\n",
            "    (FC_hidden2): Linear(in_features=400, out_features=400, bias=True)\n",
            "    (FC_output): Linear(in_features=400, out_features=784, bias=True)\n",
            "    (LeakyReLU): LeakyReLU(negative_slope=0.2)\n",
            "  )\n",
            ")\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "# 3. Define Loss function (reprod. loss) and optimizer\n"
      ],
      "metadata": {
        "id": "yWfvW3k1xwNj"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "from torch.optim import Adam\n",
        "\n",
        "BCE_loss = nn.BCELoss()\n",
        "\n",
        "def loss_function(x, x_hat, mean, log_var):\n",
        "    reproduction_loss = nn.functional.binary_cross_entropy(x_hat, x, reduction='sum')\n",
        "    KLD      = - 0.5 * torch.sum(1+ log_var - mean.pow(2) - log_var.exp())\n",
        "\n",
        "    return reproduction_loss + KLD\n",
        "\n",
        "lr = 1e-3\n",
        "optimizer = Adam(model.parameters(), lr=lr)\n"
      ],
      "metadata": {
        "id": "ei9Ff4WTxrAM"
      },
      "execution_count": 7,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "# 4. Train Variational AutoEncoder (VAE)"
      ],
      "metadata": {
        "id": "bGkr4lk-x5TD"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "print(\"Start training VAE...\")\n",
        "model.train()\n",
        "\n",
        "epochs = 100\n",
        "\n",
        "for epoch in range(epochs):\n",
        "    overall_loss = 0\n",
        "    for batch_idx, (x, _) in enumerate(train_loader):\n",
        "        x = x.view(batch_size, x_dim)\n",
        "        x = x.to(DEVICE)\n",
        "\n",
        "        optimizer.zero_grad()\n",
        "\n",
        "        x_hat, mean, log_var = model(x)\n",
        "        loss = loss_function(x, x_hat, mean, log_var)\n",
        "\n",
        "        overall_loss += loss.item()\n",
        "\n",
        "        loss.backward()\n",
        "        optimizer.step()\n",
        "\n",
        "    print(\"\\tEpoch\", epoch + 1, \"complete!\", \"\\tAverage Loss: \", overall_loss / (batch_idx*batch_size))\n",
        "\n",
        "print(\"Finish!!\")\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Tdj9giA2x4d2",
        "outputId": "4777d20a-2208-4c41-c34a-e217233291f2"
      },
      "execution_count": 8,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Start training VAE...\n",
            "\tEpoch 1 complete! \tAverage Loss:  174.45327430483096\n",
            "\tEpoch 2 complete! \tAverage Loss:  128.95353152063333\n",
            "\tEpoch 3 complete! \tAverage Loss:  116.99807053096306\n",
            "\tEpoch 4 complete! \tAverage Loss:  112.41056456398685\n",
            "\tEpoch 5 complete! \tAverage Loss:  109.99989539858097\n",
            "\tEpoch 6 complete! \tAverage Loss:  108.46988700242592\n",
            "\tEpoch 7 complete! \tAverage Loss:  107.31140675539963\n",
            "\tEpoch 8 complete! \tAverage Loss:  106.33424741104966\n",
            "\tEpoch 9 complete! \tAverage Loss:  105.54594609179361\n",
            "\tEpoch 10 complete! \tAverage Loss:  104.84990464250313\n",
            "\tEpoch 11 complete! \tAverage Loss:  104.29589620395973\n",
            "\tEpoch 12 complete! \tAverage Loss:  103.85685251786832\n",
            "\tEpoch 13 complete! \tAverage Loss:  103.48037993009181\n",
            "\tEpoch 14 complete! \tAverage Loss:  103.10478734088063\n",
            "\tEpoch 15 complete! \tAverage Loss:  102.8120355540484\n",
            "\tEpoch 16 complete! \tAverage Loss:  102.53921904345785\n",
            "\tEpoch 17 complete! \tAverage Loss:  102.31260174835664\n",
            "\tEpoch 18 complete! \tAverage Loss:  102.0246276019929\n",
            "\tEpoch 19 complete! \tAverage Loss:  101.83749980436144\n",
            "\tEpoch 20 complete! \tAverage Loss:  101.68595003717132\n",
            "\tEpoch 21 complete! \tAverage Loss:  101.50466658297684\n",
            "\tEpoch 22 complete! \tAverage Loss:  101.34194939156407\n",
            "\tEpoch 23 complete! \tAverage Loss:  101.2154644622548\n",
            "\tEpoch 24 complete! \tAverage Loss:  101.06151883999374\n",
            "\tEpoch 25 complete! \tAverage Loss:  100.91478333029006\n",
            "\tEpoch 26 complete! \tAverage Loss:  100.84193284380217\n",
            "\tEpoch 27 complete! \tAverage Loss:  100.68952110940108\n",
            "\tEpoch 28 complete! \tAverage Loss:  100.58466955016173\n",
            "\tEpoch 29 complete! \tAverage Loss:  100.49636725271286\n",
            "\tEpoch 30 complete! \tAverage Loss:  100.40875404319699\n",
            "\tEpoch 31 complete! \tAverage Loss:  100.34908566686666\n",
            "\tEpoch 32 complete! \tAverage Loss:  100.23554496752399\n",
            "\tEpoch 33 complete! \tAverage Loss:  100.17211297801022\n",
            "\tEpoch 34 complete! \tAverage Loss:  100.0998343430457\n",
            "\tEpoch 35 complete! \tAverage Loss:  100.0144510870983\n",
            "\tEpoch 36 complete! \tAverage Loss:  99.94320043496974\n",
            "\tEpoch 37 complete! \tAverage Loss:  99.93468753260643\n",
            "\tEpoch 38 complete! \tAverage Loss:  99.84449354066673\n",
            "\tEpoch 39 complete! \tAverage Loss:  99.77064932439482\n",
            "\tEpoch 40 complete! \tAverage Loss:  99.70877419396912\n",
            "\tEpoch 41 complete! \tAverage Loss:  99.64979632395138\n",
            "\tEpoch 42 complete! \tAverage Loss:  99.57612109048935\n",
            "\tEpoch 43 complete! \tAverage Loss:  99.51912670205552\n",
            "\tEpoch 44 complete! \tAverage Loss:  99.46414928200647\n",
            "\tEpoch 45 complete! \tAverage Loss:  99.42987837802588\n",
            "\tEpoch 46 complete! \tAverage Loss:  99.34950299653067\n",
            "\tEpoch 47 complete! \tAverage Loss:  99.34110521115922\n",
            "\tEpoch 48 complete! \tAverage Loss:  99.24755128991026\n",
            "\tEpoch 49 complete! \tAverage Loss:  99.2662976379904\n",
            "\tEpoch 50 complete! \tAverage Loss:  99.1619426420336\n",
            "\tEpoch 51 complete! \tAverage Loss:  99.18076525654737\n",
            "\tEpoch 52 complete! \tAverage Loss:  99.08274340698038\n",
            "\tEpoch 53 complete! \tAverage Loss:  99.06012775198248\n",
            "\tEpoch 54 complete! \tAverage Loss:  99.02367353792779\n",
            "\tEpoch 55 complete! \tAverage Loss:  99.01523488039962\n",
            "\tEpoch 56 complete! \tAverage Loss:  98.98435667518781\n",
            "\tEpoch 57 complete! \tAverage Loss:  98.92438981962124\n",
            "\tEpoch 58 complete! \tAverage Loss:  98.88181929191882\n",
            "\tEpoch 59 complete! \tAverage Loss:  98.86332300253027\n",
            "\tEpoch 60 complete! \tAverage Loss:  98.82977623839211\n",
            "\tEpoch 61 complete! \tAverage Loss:  98.8213923270555\n",
            "\tEpoch 62 complete! \tAverage Loss:  98.74706662797371\n",
            "\tEpoch 63 complete! \tAverage Loss:  98.73043519798622\n",
            "\tEpoch 64 complete! \tAverage Loss:  98.728669967524\n",
            "\tEpoch 65 complete! \tAverage Loss:  98.58638709372391\n",
            "\tEpoch 66 complete! \tAverage Loss:  98.61584093606531\n",
            "\tEpoch 67 complete! \tAverage Loss:  98.55381892998749\n",
            "\tEpoch 68 complete! \tAverage Loss:  98.55535783923727\n",
            "\tEpoch 69 complete! \tAverage Loss:  98.56289165210246\n",
            "\tEpoch 70 complete! \tAverage Loss:  98.48535138316466\n",
            "\tEpoch 71 complete! \tAverage Loss:  98.51491504395347\n",
            "\tEpoch 72 complete! \tAverage Loss:  98.47481292062291\n",
            "\tEpoch 73 complete! \tAverage Loss:  98.45185008868948\n",
            "\tEpoch 74 complete! \tAverage Loss:  98.47508630921327\n",
            "\tEpoch 75 complete! \tAverage Loss:  98.39354343828255\n",
            "\tEpoch 76 complete! \tAverage Loss:  98.35606256195221\n",
            "\tEpoch 77 complete! \tAverage Loss:  98.31566826872913\n",
            "\tEpoch 78 complete! \tAverage Loss:  98.33404921288084\n",
            "\tEpoch 79 complete! \tAverage Loss:  98.28071703164127\n",
            "\tEpoch 80 complete! \tAverage Loss:  98.27722807869887\n",
            "\tEpoch 81 complete! \tAverage Loss:  98.21675403015442\n",
            "\tEpoch 82 complete! \tAverage Loss:  98.23511391055405\n",
            "\tEpoch 83 complete! \tAverage Loss:  98.19540035801857\n",
            "\tEpoch 84 complete! \tAverage Loss:  98.19136395946369\n",
            "\tEpoch 85 complete! \tAverage Loss:  98.17317384442822\n",
            "\tEpoch 86 complete! \tAverage Loss:  98.19650814508556\n",
            "\tEpoch 87 complete! \tAverage Loss:  98.12958475714733\n",
            "\tEpoch 88 complete! \tAverage Loss:  98.1430884318917\n",
            "\tEpoch 89 complete! \tAverage Loss:  98.14626677600688\n",
            "\tEpoch 90 complete! \tAverage Loss:  98.0849345099906\n",
            "\tEpoch 91 complete! \tAverage Loss:  98.01591001278172\n",
            "\tEpoch 92 complete! \tAverage Loss:  98.05309526293823\n",
            "\tEpoch 93 complete! \tAverage Loss:  98.0545669866444\n",
            "\tEpoch 94 complete! \tAverage Loss:  97.99499613613835\n",
            "\tEpoch 95 complete! \tAverage Loss:  97.9743212809109\n",
            "\tEpoch 96 complete! \tAverage Loss:  97.96107325686039\n",
            "\tEpoch 97 complete! \tAverage Loss:  97.95209951155572\n",
            "\tEpoch 98 complete! \tAverage Loss:  97.98564247704508\n",
            "\tEpoch 99 complete! \tAverage Loss:  97.926271210481\n",
            "\tEpoch 100 complete! \tAverage Loss:  97.93489838206908\n",
            "Finish!!\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "#5. Generate images from test dataset\n"
      ],
      "metadata": {
        "id": "CtMaHstsyMFf"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "model.eval()\n",
        "\n",
        "with torch.no_grad():\n",
        "    for batch_idx, (x, _) in enumerate(tqdm(test_loader)):\n",
        "        x = x.view(batch_size, x_dim)\n",
        "        x = x.to(DEVICE)\n",
        "\n",
        "        x_hat, _, _ = model(x)\n",
        "\n",
        "\n",
        "        break\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "nPT_EQQayLxZ",
        "outputId": "3fdd8198-dda9-4de7-fd18-ff5d3f4e6aff"
      },
      "execution_count": 20,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "  0%|          | 0/100 [00:00<?, ?it/s]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "import matplotlib.pyplot as plt\n",
        "\n",
        "def show_image(x, idx):\n",
        "    x = x.view(batch_size, 28, 28)\n",
        "\n",
        "    fig = plt.figure()\n",
        "    plt.imshow(x[idx].cpu().numpy())\n"
      ],
      "metadata": {
        "id": "JSkE008byUuk"
      },
      "execution_count": 21,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "show_image(x, idx=0)\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 430
        },
        "id": "-F2KCE20ybyb",
        "outputId": "a79cccce-70d1-427b-d946-9709400c7092"
      },
      "execution_count": 22,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "show_image(x_hat, idx=0)\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 430
        },
        "id": "DLKO9ZE0yeD0",
        "outputId": "14a714b0-60ae-47fd-d32f-bcffbb79ab41"
      },
      "execution_count": 23,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "# 6. Generate image from noise vector\n",
        "Please note that this is not the correct generative process.\n",
        "\n",
        "- Even if we don't know exact p(z|x), we can generate images from noise, since the loss function of training VAE regulates the q(z|x) (simple and tractable posteriors) must close enough to N(0, I). If q(z|x) is close to N(0, I) \"enough\"(but not tightly close due to posterior collapse problem), N(0, I) may replace the encoder of VAE.\n",
        "\n",
        "- To show this, I just tested with a noise vector sampled from N(0, I) similar with Generative Adversarial Network.\n",
        "\n"
      ],
      "metadata": {
        "id": "HM9jXcyNygcz"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "with torch.no_grad():\n",
        "    noise = torch.randn(batch_size, latent_dim).to(DEVICE)\n",
        "    generated_images = decoder(noise)\n"
      ],
      "metadata": {
        "id": "6XjX-y311EYR"
      },
      "execution_count": 24,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "save_image(generated_images.view(batch_size, 1, 28, 28), 'generated_sample.png')\n"
      ],
      "metadata": {
        "id": "S0snCfEC1IaS"
      },
      "execution_count": 25,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "from IPython.display import Image\n",
        "Image(filename='generated_sample.png')\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 409
        },
        "id": "1am7x7Vz1p2K",
        "outputId": "ce5e43ce-fecf-43b9-821a-4a5079ad272e"
      },
      "execution_count": 26,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "image/png": 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T6XSz2dzQ0BAWFtbU1GSz2WDCrnQAd4Z1gUqlLl++nMViOZ3OgoICL07MABKJNGfOHB8fHwh+BQQEJCcnh4SECIVCsKpNJlNMTExDQ4NarbbZbCiK2u122HAkEklnZ6fBYHDzWuCIs1gs//jHP65evTp16tSPP/544cKFH330UXd39xBfHEZbW63WkpKSsrIy5IZrdsqUKRiGHT58eNiN4E4YGBh49913aTSan58fGMEYhtHpdC6XSyaTjUZjREQE2GEDAwNXr171VKkMPSs6ne7j4wNnA/fdOAaDoaSkBMIlra2tRqMRdhgOh7NmzRqxWNzd3f35558XFhbC2+56uzxaIrVa3dTU5HQ64+LiuFwuhULBMIzP5/v6+mo0GpVKBS8k7EvuD4sgCIqiubm5sbGxBEHo9fqhZWJoOByOtra2rq4uJpPZ19c3MDCg0WgsFsuYMWMg0EMmk3Nycng8Xnd3N5xZ9Xq9UCgcM2ZMT0/Pt99+675YYxh2zz33cLlcCDWcPn1aLpf7+vqGhIT09PSMNCfE9fgxDFu/fr3dbn/xxRdHEvR3Op1Go7G1tdV1WKZSqXa7HeJhIN8Igmi1Wo1G434IGs5wQzjqURTNysricDgqlcp9r6rT6Tx16pRSqQQ3MDhTwQ3C4/Gys7OtVuvrr79+4sSJW3dGNy9BIpHYbDaFQpHJZGq1GkVRcG6CThUIBDExMbW1tSaTCawRT8Way+V+9tlnGIYNDAxUV1dLJBKBQCCXy70zZgoKCo4ePTp+/Pje3l6tVstisTo7OzkcDolEAgd5eHh4cHBwV1cXRDqvXbsWFBTEZDLj4+MvX77svqeBw+HMnDnzzz//BGVBIpHAKOXxeCOyrW9CXFwcm83u7+/v7+/36It3gkufuawaEok0ZswYHMcRBMEwzP1zOsR66HQ67H23/QydTn/55ZfBvej+LRAEoVQqq6urtVrtYJlms9kPPfRQQkLC/v37byvTbgLDMDabLRQKDQaDXC4nkUgWi2XmzJk0Gq23t7e1tbWqqmpgYABcy2C4ezQ+juMbN27kcDgmk+nEiRNXr17NyMhYtGjRDz/84HJX3+SmGFpodDrdd999p1AoAgMD2Wy2Xq8HOQNFXl1dTaPRGhsb+/v7Qe5bW1sNBgOZTI6NjW1oaHBz2mDthISEXL9+HSyFadOmxcbG6vX6Yc/6non1448/juP4jz/+OJJT+W0xeEAwZEEruJ/YieO4SCQCra9Wq2+dIZlM/vrrr+Pi4mQy2aeffuq+FMID6+3tdXmpweZ77rnnFi5c+Oeff77//vsj8cGBI8xiseh0OjiUW61WhULR3d197dq1X375pbOz03WS8dSwRlFULBZPnTrVYrE0NTX9/vvver0+Li5u0aJFGo3m5MmTer0e3tJhjyUuOJ3O9vb2nTt3+vv7g8ctMzNTq9V2d3f/9ttvtbW1NBpNoVCAI8hoNLr2z66uLvf3GaFQCHFAjUaD43hgYOD7779Pp9MvX748rBHlgViTSKQVK1Y4nc5vv/3W/W95CgzDBAIBgiDgJ/Lo/ZFIJNnZ2ZWVladOnbpJpdHp9N9//33mzJk2m2379u0FBQUejez6MI7jkD+0adOmJUuWdHV1vfnmm14fv1yg0WiQbMjhcMLCwnJycpKSki5fvrx79244LA6OWHk68qOPPhoTE2O32wcGBiQSCYfDGTduXEREBMR9Dhw44PJEeRRoNBqNLS0tbW1tOI5XVFTQ6XQmk6lQKMBMcm0Cg11S7ss0hmHJyckSiUSlUiUnJwcGBq5bt04oFLa2tm7dunVY69wDsQ4ODmYwGGVlZe3t7e5/y1NwuVzwWDudTrVa7f4XyWSyw+GYN2/epk2bXnzxxSNHjhiNRvAxSSSSI0eOJCQkOByOM2fO7N2711NBJAgCzESJRDJ9+vR58+ZlZGQ0NTU9+eSTAwMDnt3hvwLSdBcsWPDII49wOByCILhcrt1ur6ur27t3b0NDA+wD3m2PYN7Ex8dDhCg2Nnbt2rU8Hs/f3x/cNWQymUKhuLYa2IjcPzXBPubKy9VoNPDzTWkFXsycSqWmpqb6+voKhcLXX38dx3Eej9fa2vrMM8/clLZwW3gg1q+99hpBEIcPH74rhQ93AigtMCogXO/OtwiCMJvNer2+oaEhNjb2o48+evrppzs7O+12e0hISGBgIIvFUiqVP/3007Zt27xLTIU3jU6nx8bG+vn5VVZWvvDCC01NTSO0x1yFXiEhIUwm026363S6y5cvf/jhh9XV1XfKPXIzRAW2eEVFRUJCQnh4uEQiAe8TgiAGg+HcuXPl5eUu8wb+9SIPbLB1dKe/egpIpbLb7QKBwMfHR6vV5ufnb9u2ra6u7m6KH47jtbW1BoNh7dq1d23Q2yEzMxPi/haLJSIiwv0vgr27dOnS06dPd3d39/T0qFQqvV5vMBj6+vq+//772bNnU6lU75SH6xJMJjMgICAwMNCj2Puww9JotLCwsMjISA6HcxcLXcHdFhMT88ILL1RUVPT19el0up6eniNHjmzevDkiIgI0CDiR4CueRpH+ImAY5uPj88QTT5w7d66kpOTdd9/18fFx/9m5+zk2m93e3o5h2Pjx492POXuBrKysHTt2hIWFXbhwYdmyZTqdzv3XHcOw2NjY0NBQsE1he+3t7f3uu++uX79uMpm8jqv9j4bL9enj4yMSiQiC6O/vVygU/zdX419AIpHWrl27adOmkWg7d0ClUr/44ov+/v533nkHdIl345BIJDKZDJVg4C4cxSj+k/ir35xRjGIUoxjFKEYxilGMYhSjGMUoRvF/Ff9FPgcSieRKuBl1qd4toDdoB//TE/EG4J8FjpdFixbJZLIrV67IZDKbzTZ0GuN/i0MXUnVFIhFwfYxkKJd/cHDF0QgH9PPzW758eXBwcFZWllgsRlFUoVCcPHkyPz+/r6+vu7sbmPj+C6UHJAMqEiwWy9CsMSO5iiu9EbmRbzzyC2EYFhwcjOM4iqKtra1jxozBMOzSpUtAQWEwGO50if8isc7Ozp4+ffrBgwcvXLjg9TiuUDCJRKLRaGaz+aYqQO8AlEITJkyA+gYEQUQiEY/HS0tLo1AoTU1N33zzTWVl5QjpemHmd+VVBABfVGZmZmJiosViqaqqAi5Mj2gvhwa8Nmw228fHh8lk0ul0m82m0+kUCgUwSHm98WIYxmAwzGaz2Wym0WhdXV1yuZxMJoeHh/f399tstiGoudwiK0NvsJsCayVBEDiOOxwO90mAhgWfz1+/fn1SUpJSqbx48aJ3awHzFIvFAoGAzWZDHWF/f39fX5+nLLo3DYui6LVr13x9faEaPD8/v7e312g0SiSStLS0zMzMzZs3nzt3bv/+/V5sNSDNNBpNLBaTSCStVguzhXqCm6hUPB0WBI7P55PJZDqdPjAw0Nzc7PWYN40PeTjBwcFRUVFQh+/v7+/n58fj8bRa7ZUrV3755Zfb5r67A4IgTCaT3W7HMAxoO318fBISEqKjo3t6eoqLi1Uq1Z32hJvFGiQjKSmJzWbT6fQpU6bEx8enpKRASQ+8mlCjRRCEwWBoaWn56quvvv/++5HkHGMYNnfu3KysLCjn9E5XwazGjBkzc+bMcePGWa1WMGzsdntRUdGXX34pk8m8Xt/y8vKqqqpt27ZBFS2sJoqilZWVBQUFeXl5mzdvfvzxxxkMxhdffOFp9QqwxsycOTMuLo5EIlVUVNjtdh6PFxoa2tnZCXToSqVycB6zm9N2Op06nU4mk0E1O41Gi42NtVqtcrkcShbcL6i79ZMoigoEgvHjx/v5+anVao1GMzAwoFare3t7p0yZkpmZGRwcfPbsWY+yi2+aPyw17GAYhgF5cWxsbHx8PLAY3+mduVmsuVzurFmz3nzzzeDgYJDg23K4wG84HE5KSsoXX3xx//33z58/X6PReHcDDAbjH//4BxS2nDlzxustmM/nr1y5cv78+TweT6VSqdVqsVjM5XLj4+PFYvFbb73lJifQTYCs19v+HigcGhsbL126lJaW5uvrSyaTPRJrqMybPXv2woULQ0JCpFJpU1MTgiBpaWlRUVGZmZn33HNPW1vbjh076urqXCVw7ufrGo3G8vLyjo4OkUgUEhJCoVAmT55ssVjKy8shoQ8YXweXft1akH9bmSaRSFwuV6vV6vX6jo4O2Ka4XK6vr29WVhaZTCaTyTQazf2luNMtuA4tJpMJaNwCAwNDQ0MHBgYMBsNtjcybxVqn08XHx/v7+0PiJXGDjwvy6BEEgVpxBEH4fD5UK5HJ5IkTJ27fvv3hhx/2giIIRdGcnBygo5XJZO7Xut00CI7jCxYsmDp1Kp/PN5lMzc3Nra2tERERYWFhLBbr3nvvDQgIWLdunUKh8GL8IQDF1X19fVKp9NKlSx5Vf4HKIJPJ0dHRQqGwurr6t99+a2pqAppTgiDi4+MjIyP5fL5EImlqagKrz33nBsiETCZTKBRyuVypVKakpCxevBhaJhw4cODPP//s7e0Fm8eVw31TScudpg02UkdHh1qthteeTCYzGIzQ0FCoOLx69aqbTCxD34LrZwzDEhMTp02bFhoaGhISgmFYf3//bRf8ZrF2OBwnTpxYunSpSCTS6/V6vd7X19doNObn57e2tqpUqtOnT6tUKi6XO23atA0bNsTHx1OpVBzHZ82aNWbMmOLiYk/nTSaT58yZAxXjeXl5XrtBQDHQaLSWlpbffvvt2LFjfX19OI5HRkZOnDhx/fr1oaGhSUlJXrdPGAJUKjUsLKyhocELalMURSkUisViKS4uBqIph8NBo9GkUqlKpaLT6fCWAqWdKysaFKr7kk0QhE6nw3EczFOJRMJmswMDA11JjvByUigUOD65M3MMw4xGI1RhIghCIpFEItGsWbPmzp3rdDovX7584MCBkZfDua6F4/iUKVPefPPN2NhYDMPIZLLBYLiTGr3NkbG8vHzJkiVAPwVmRm1tLfS+QBAE/lUqlUBR9dVXXwHPE4IgMpnM0+lCYj4wXJnNZoVC4V0aOxwvqqqqjh07ptVqf/zxR6lUCo9HqVQ2NDRERkZOnTp10qRJV65c8WJLGQIkEik2NjYoKOjAgQOeckDCh6lUaldXV21tbUtLCxAGwO8jIyNDQkIsFgsU2jmdTgqFQqfTnU6nqwWM+xdyOp0sFis5OZnL5VoslpMnT+7cubOnpweq9KGVjNlshg47w94FmUwGaiuVSsVkMhkMRlpaWm5urkAgEAgECoWir6+vq6tr5H4hEGgWi/XII488/fTTQFVus9nKy8vPnDlzJ0/AbcTaYrE0NjbCzzqdbmBgAM4WN2kIu93O5/OBjw9BEJPJJJfLvZh6TEyMj48PHHjT0tICAwOHbVxyWzidzrq6uiNHjhgMBrVa7ZoqQRAajWb//v1jxoyJj49nsVh30YGDoqi/v/+yZcsMBoMX9UigqkUikYs6ApiA4uLicnJylixZwmazy8vLjx8/brfb6XR6cHBwSkoKnJaam5t1Op2bV4TC5y1btsyYMcNqtZ4/f/75559XKBSudXat1bD+ZtDuTCZzxowZs2fPBv7ihIQEp9PZ09Mjl8thSkAE7NFq3HbaQqEwMjLy/vvvv++++1gsFoqiJpPp/PnzTz755BAb+zAOvsGnpcEriKIol8t97LHHIENfoVCsWbPGC/Z5BoORmZmJoqjVaiWTySEhIePHj5fJZOC78Wgop9Op0WiKiorA5hv8dafT2dTU1NTUxOPxxGIxCL2nU70VKIqyWCzoQHX48GH3mXoGjwC8ctHR0RwOBxxB0dHRaWlpU6ZMEYlEcrm8vLwcum+FhobOmzePTCYDaeXu3bsrKircuQqcSh988MF58+ax2eyysrIPP/xwcB8F17/DCiLsJCwWa+zYsUuWLAkODqZSqSwWq6Wl5ezZs2fPntVqtWFhYS+//HJ2dvYff/xx5swZrzUIfBH2galTpwJllMFg+Pjjj7dv365Wq4d4pb0Jx0DUbceOHQkJCbBhvfjii5cvX/bioVIoFD6fr1KpZDIZjuONjY1jx441m82HDh3yQmFDRSos/U07qd1ub2pqCgkJ8fX1BXb3EYY8QKYnTpxIoVCOHz/e3t7uxYRRFOXz+ampqdDmJycnB8dxcNDCkWhgYEAmkwkEAi6XKxQKFQqFTCaj0WjAsOrmJXAcDw8PHzNmjM1mUygU/f39sbGx0FgDSEJcC+X64abVG8wiAj8TBNHa2nr9+vULFy50dHRAaw5QFna73cfHRyKR+Pr6erogN4EgCCqVGhMT4+/vD5yUNTU1X3zxhUqlGlE3gtuCTqf//PPPGRkZwPRaWlq6d+9eL6QEdBWCIFVVVRcvXoT9JTc3Nzo6msVieefvBCMSXDSu4zyJRKLT6XK5nMViCYXCsLCw5uZmV+jVu0gHl8udP39+RESEXC6HZjHeqSWTySQSifh8PoIgAoHAZDIZDAbo8aXT6dra2np7e/v7+wcGBiwWC4vF4vF4TqdTLBbfibnq1qkC/TaFQoHOBF1dXZmZmRKJZO/evYjbHhWXNKMoarPZWlpa9u3bB3SEg90mKIrS6XSxWOx0Oru6urxYkMEAIyQ6Ohr8ATab7dlnnwU9PfS0PRZrHx+fEydOACuu0+n8/fffH3jgATeX+CaAImlvb29ubq6trWUwGJGRkT4+PtnZ2Xv37vXajY/csP+oVCqE0Hk8Xlxc3PTp08eMGZOent7W1lZYWHjt2jWpVGqxWKxWq4vswk2QyeSgoKCgoKDAwEAMw8B+8GKeQB9+6tQp6O6g0+ksFotEIqHT6b29vSdOnDh37lxVVRV0T8QwzGQyQfIJSDmO40OvPKwwj8dDEKS3t7e2tra8vFytVqenpwcFBYE9dquI3PZeBguu3W6XSqW9vb23BnRQFJ01a5ZQKJRKpVDK7c4B9LYgkUj+/v4vvfTS5MmTYQeurKwsLy93xwXkmVjz+fyioqLg4GC4TF1d3QMPPABNBbwD2MGNjY1arVYoFGZnZ7NYrIaGhpFkO4FLi0ajpaSkLF++PDw83OFwsFisoKAgLpfL5XIFAkFycnJCQkJdXV1paanVaoVcJTfHhxO6Wq0+ePBgUFAQMIVyOByz2QycMh4FAo1G4zfffHP58mWbzcZgMJKSkqZOnWo2m8+ePfvnn3+2tbW5nB4udzU0VnQ4HEqlcth5MhiMjIyMtLQ0KpVaVlZ27do1OGDQ6XQOh4Pj+K2209AeaxzHwRt4q3ihKBoVFfXcc88hCHL9+nXXAclTyQatFBUV9fXXX6enp+M4DlxI69atc7PHjQdiTaVST548GRgYCLNUKBT33nvvSGQanKngwYF0Aug9VV5e7nUvUNfIZDJ5+fLlkyZNQlG0v78/ICCARqPZbDYIHQP9pMFgUCqVSqXSffcqRCJsNltvby9BEG1tba2trcHBwdOnTxeLxRcuXGhqahrshBl2QOg0d+3aNQaDwWKx/P39Ozo6tFrtoUOHOjo64D2BFDaXtwu64bgT+iaTyWKxOCcnZ+zYsfX19U1NTRaLBUVRGo0Gr4r7nCSuNCzXD7d+hs/nf/TRR1wut6ys7N133/WuSyCkoa5YseKpp54CYXM6nR0dHQ8++GBjY+NtB7z1tXFXrH19fQsKCkJDQ+GWtFrtpk2bBu8y3u01EMqJjY0dGBiYMWNGaGioTqeDzENPh7oJVqv1t99+q6ioAP7ZgIAADMN0Ol1nZ2dzczMwrkOAyX32yttmXep0uoCAgBUrVhiNxqKiItcO7n58G84DFouFTCa3tLRwOBy5XA7UjNCj0eFwQMTEbreD8e2O1QTDgqoDCl0qlcrlciMjI5lMplKptNvtbmaAuaKhwNgGCvsmNc/n83fu3Jmamtrb2/v2229XV1d7d9wSiUTff//95MmTIVnS6XTKZLIlS5ZUVVXdacBbb8Etsfb19c3Pzw8LCwOZlkqlb7311rFjx2DRkRsvvRdibbVaRSJRfHw8EMIzGIwTJ05UVlaO3K9sNBovXrxYWFjo6+sLHLgIgsjl8vz8fEge6u3tBV3ojlkMmy+ZTHbJATxpGo2Wm5s7Y8YM8Ic0Nja6EqFcXxz2XohBLUHA0Ql7IPwS/gqE7eBxv5Xn7k6ABMaioiIfHx+r1Tpp0iSz2TxnzhyRSNTZ2dnZ2emm+iBu5GwiCEKhUCB7x+X+hwP09u3bMzMzOzs7N2/eXFRU5J1iwjBs/vz5rgRgh8PR3d29cuXKIWT6thherPl8fn5+flRUFFymp6fn6aefvnjx4uAtxjspdDqd4LHKyspKTU1lMBhyufyTTz4ZYWMr15QgDgznsJaWFgzDzp07d+nSJcjO8YgmFNx5UVFRGo0Gum1DTthjjz0WERHR3t5+6tSpc+fO3eQWcJ8pD6ym4OBg6AIMxObw9ZsmOdjBPOzMwSTNy8uz2+1jxowZM2ZMcHCwv7+/XC6vqqpy/ziBIIirUYbNZuPz+RCVdDgc4Fd+9tln4+Pj+/r6Hn/88YqKCq83WzKZPGvWLPB7OJ3OxsbGVatWeSrTyLBiTafTCwsLoTmi2Wy+du3a5s2bm5qaPOpOOQSMRmNxcXF2djaI+O7duxsbG+8udSVBENXV1QwGQ6fT1dbW9vf3uwjQ3L8FDMMSEhLeffddX1/f7u5uuVw+fvx4Hx8f0Kz79+//+eefoa/z4G+5b94gCMJkMhMTE9PS0qxWq1arhcS6m27EUwsHuaE7/vzzT5FINGnSJKFQqNfrf/311z///NOjHHTXilksFoPBQKFQIiMjAwMD58+fP3XqVB6P19LSsnnzZk87CN8EIH4HJ8/58+dXr17tHQ/oUGLNZrOfffbZwMBABEHgkPT222/X1dXd6lRyP6fsJjgcjqampo8//ri0tLSlpeXixYt3N2EDQRCTyVRaWgoNh1QqlU6nc9lO7p8H4HRYUFCQk5MTHBwMxPIKhaKlpeUf//hHSUnJSIqpXF8EUe7o6Ghvb4fA+E1jQkgCfkmj0dwM6zocjv7+/p9//rm1tdXf37++vv7KlSt6vd47+bPb7SqVSiQSiUSi2bNnJyQkdHd3Hzp0aPv27X19fbcd0/11djgce/fudTgcCoVi586dXnsObmNWwiRIJNLWrVsffvhh2HEUCsWXX3759ddf3xoiBoN7JMrbCyXk/shQ1yMSiYxGo06ng31m8OHP0wG9/u4QY5JIpICAgIyMjLi4uPb29gsXLkAS0uCr4DhOIpEge8TNhKTBlyCTySwWi0KhqNVq72qFXI8JWCqnTZs2ZcqU8vLyP/74o7e314sg61+H22hrkGk6nb5w4UIymWwymcxmM7RaupM7z2uXu+uKXn932JEhNxBBEJvN5tpnIFnHZDJ5ujncRWm+aVhoe97b2yuVSgcGBiBWOnhjcZ1uPbWgkBtJ4RBvH+GuAlSdOp3u2rVrDQ0N9fX13jny/lLc0QmAomhWVlZKSkpRUZFYLE5MTPz+++/7+vr+q15KNwHq0LU/un4Y4dt4FwHRfnCcuX552xjef8mEkf/hVA2jGMUoRjGKUYxiFKMYxShGMYr/HOCY/p+exSi8BYqiDAbj3nvvfeSRR86dO5eQkHC3WnVBrtzIKwL/nXBlGroc/P8R/Ldw8P0VAIXBYrEEAoFGo9FoNHfdO0kikeLi4l588cWZM2dSKBSZTKZWq8lk8girgDEMmzhx4ssvv0wikS5fvvzZZ5951PEMQRAoUB/aK3/XPXToDRpLHx+fpKQkqB/1OpYOLwaEULhcLuSNQorVsJUEHoj14AAb/Oav8FlCbrF35TYuQJXkpEmTVq1alZGRAYkQhw8f/uCDD7ymLLvtVYBNITo6miCIurq6zz77DGhqRzgylUqdPHlyYmIiECMdPny4rq7O/XcS2D/ulDEGqhTEBUju7kqMCdY8Li4uNzdXIpHk5+drNBo3k71uBeijkJCQJUuWjB8/HiqGbDZbc3Pz8ePHjx49Crkid5r58GJNIpGEQmFOTs6kSZMSExN9fHzMZnNfX19LS8vp06evX78Odfl3hW93woQJ+/btk8lk99xzz0jolzAME4lEc+fOHTduXFBQEJVK5XA4M2bMOHjwoFwuv4tiLZFIpkyZkp+fn5eXV11dbTQaR74h4Dg+e/bszZs3i0QiBEFiYmLWrl37+uuvuz8yiUS6bW0l9PAMCwtDUdTHxwfDMI1GI5fL29ragCEEGYGqQlE0KCjoiSeeSE9Pl8vlx48fd6XfeDom1NEtXLjwscceCwgIsNlsJpOJRqORyeSwsLA1a9aMHTv2119/hRJSxIsyAgzDoqKi3nrrrYkTJ9LpdIfDYbfboTxJLBYnJCQUFhbm5eU1NjZCTqanazEYdDr93XffDQsL4/F4PB7Pa7FGUZTH4z3++OOzZ8+G6gGYNgTM75bBB/XFixYt6ujoOHXqFDDXjPzdJpFIM2bM+Pjjj4VCISQ20en01NRUoVDofoz61mIfYATOysp6+eWXBQIBkIy1t7eHhoaSyeT29vbvvvsObsG7WmM4YCxbtmz8+PFMJrO7u1un03ndrZ1KpU6dOnXlypVsNrulpaWgoOD69etqtRoah0+cOHH8+PGzZ89ubm6GDB/PyghQFBWLxR9//DFkS1ZVVZ05c6ajowNaLAcGBmZkZCxZsiQqKmrfvn2FhYWQBeVdgBdFUYFAkJiYiGGYwWDQarVeB4pRFA0ICBg3bpyvry+KolqtFozdmpqau5j1SqFQsrOzeTxeQUFBZ2cnpB+NcEwcx+fMmfPdd9/xeDwURS0Wi9FoJJPJsbGxc+bM+fbbb73bCmCEl19+eebMmUBXZDab1Wq11Wptbm5OSEgYP358cnLyN998U1BQ0NPT4wXDGI7jEyZMSEtLYzKZOp2ut7cXiuK8mC28gTNmzKDT6efOnfv111+rqqpcNAFkMtnpdC5evJjH4x05cqS/v//28xniAjQa7amnnpo8ebLD4WhoaNi6dWtLS4vT6fTz8xMIBBiGSaXShISEKVOm2Gw2vV5fXFzsNecaiqLjxo1js9kIgjQ2NgJ/hXdDkcnkefPmhYWFMRgMIIsyGAxOpxPqzL0b81ZQKBShUNjX19fX12cyme6KTC9atOjzzz8HXkm1Wl1cXIzj+Pjx4wUCwbp1644cOQLlBR6BRCKlp6d//vnnkZGRVCoVqDbefvvtsrIyqMRJSEiYOXNmfHy8SCQSi8VesCBgGBYYGJiTk4NhWFNTE5fLra6u9pocHnJjNBrNn3/+WVRUVF1d7SKvgp12zpw5wcHBOp1uCMV3R7EGwzE7OxvHcYvFUl1dLZfLGQxGWFhYQkICh8Ph8/nQVJxGo4WEhAQFBRUXF3utYmk02vr166EQeufOnV7LH6jqpUuXBgcHk8lkgiAcDgeFQtHpdAiCCASCu2VbQ3FhS0vLXUn/wjBs+fLlH330EfQkVygUn3322bFjx+Li4qKionx9fZOSkjZs2PDmm296ysgaHh6+e/duINMxGo379u17/fXXVSoVOBNQFJXL5YGBgYGBgeA88dRIQ1GUyWQ+/fTT48aNq6ur6+joEIvF58+f91oxQTJjUVERj8cD1nrkRlUhmUy+7777VqxYQSaT+/v7a2pq7qRN7ijWOI4HBweDYwUohJOSklJTU9PT09ls9sDAwMWLF+vq6oxGo7+/v1arraioGEk7C19fXygzlkqlZ8+e9XocHMfj4+OhbgVBEIIgGAwGrG9mZqZWq/3iiy/uimSzWCwymXxX8oxRFA0ODn7hhRf4fD5o040bN5aUlBAE0d3dnZ6e/thjj1EolDVr1vzwww8uekR34OPj8+2334JMK5XKDz744PPPPx9c2UQQhNlsLiwsDA0NjYqKMpvNNTU1HukU2A2AfaWgoIBGo5WWljY3N3vdSQf8kpcvX05JSbFarXw+n8Fg2Gw2JpO5bNmyVatWUalUqVS6atWqIYrWhtLWYPVbLBatVuvj4wPOELFYbDKZiouLz58/r1KptFrt0qVL6+rq3C/hvu21Jk6cGBQUhCBIYWEhaFbvxoGzCzitHA6Hw+GwWCwajQZ6QTz22GN0Ov3ll18eYbkkiqKuana46EjeEw6H8/7770dERCAIUl9fP3/+fKlUCoupVqt///331atXCwQCiUQybdq01tZWN18kHMc//vjj9PR04M154oknDh06dOuNO53O5ubm06dP79q1i0Qi3Xfffbt373Z/8jwe77777jMajYWFhb29vRwOp6qqaoQZ2MDdKpPJQkNDc3Jyxo8fT6FQWCyWSCQikUiVlZVbtmxpaGgY4hJ3jIfZ7XalUllTUwMcSAUFBd3d3cAo3NHRUVxcrNfrRSJRUFAQnG+GaLs0LMhkck5ODpfLdTqd33zzzUjy3J1OZ3d3N9QsNjc3//DDD48//vimTZsuXLjAYDAEAsG9994rFApH6A+B9iPFxcUuumGvB6RSqZ9//vnMmTOhicSKFSugBNjllJVKpaCWcBxfuHAhnNfdGTkpKWnRokXgTjly5Mjx48dvW60HVgSLxWKz2VlZWYsXL3b/XlAUTUhIiIyMbGlpKSoqAvp676oPb4LFYlEoFCKRKDc3NyMjY/z48aGhoVQqFVg8hzA/AHfU1k6nE7yPhYWFlZWV7e3tJBKpuLg4KCiooqLC6XSOGzdu+vTpiYmJSqVyhEW7EokEGscYjcYRsikAHe3x48dra2vPnTtXUFAAp9jGxsacnBwqlcrj8YKDg6VS6UiukpycPG3atPr6evAYAqsi0DN4NA6GYY8++uiCBQuYTKbZbP7999/b2tqIQaW4UP3AYDAQBCEIwsfHh8FguOODw3F827ZtFAoFzsrffPPNrTIN5XAMBkMikSxYsMDhcAiFQoFA4P78KRTK/fffTyaTy8rKOjs7w8LCjEbjXeFZdjgcQBfY2NiI47jVam1tbQ0LC/P39582bdr3338/dJnjUJ4Qk8l0+fJl4DgEsjaZTAYRLH9//7CwsIkTJ4I34Ny5c15v6yiKrlu3LiAgAEGQb775ZmgCrmEBxiLwzBcVFbkkQKPR9Pb2CoVCBoMxd+7cqqoqr8kgyWTy1q1bExIS1q1b5+vrC3bItWvXysrKPGJTh0P5U089xWQyEQQxGAzFxcXQa8oVhebz+cnJyRQKBWwqq9XKYrGG6HDlQmho6JgxY8AMKy0t7ezsdLHJABtOZGRkWlrawMBAa2srhUKBF4BMJiclJVGpVDc9WmKxmMViSaVS8Jw6HA4oC7xtWN5TU81ut1dUVMhkMjidYxg2Z86cBx54ICAgICoqqre3d4jvDiXWBEEYDAbY9Zw3AAxDGIaNGTNGIBAYjcYffvjBZQt6ARKJlJKSAowqv/3228j5eTEMCw8PJwjCdfQBKQECSDjisNlsL9i4kRu1cFOmTIH2HTk5ORDCaG1tTU5OrqysdL8hAYVC2bRpk7+/P7ioq6ur2Ww2dKICpiE/Pz+HwzFhwgQIJ4E4BgQE9PT0DPvyLFy4EHYSo9HY2dnp4+PD5XKhb6Kfn9+qVat4PF5tbe3p06eNRiOTycRxnEKhoCgKSRfuzB/DsJiYGDjJ+Pj4xMfH5+bmXr9+HTzWLplxrZs7YyI37CLo6IdhmEwmM5lMsNUYjcakpKSEhAQguh9iEYYPxwBtrkajsdlsOI7T6XSIRMTExKAoeubMmTNnzozEG4DjuJ+fH4qiZrO5ubnZ63EAJBIpISFhxYoVzc3Nhw8fdgVXo6Oj4SrAeQeZJ4jnMTBoSgbcX/X19d98801tbS2XyxWJRAsWLDCbzeDBcGcoKpWakZEB8YWurq5jx47l5+cTBDFv3ryoqCiJRKJQKJqbm+l0ulqtBn8OQRDQYXHYtJOgoCAmkwmhjUWLFvn7+7PZ7NDQUHDhW63WkydP7t6922AwwHsOvfP0er37RiCGYaGhoSKRiMvlbtq0icPh8Hg8Mpksl8sdDgebzS4pKQE72/2wPEzY39+fwWDo9XqbzWY2myFHyOl09vX1NTU1paSkhIWFUanUIfbbocSaTCaPHz8+Nzf38uXLp06d0mq1OI5zOJyEhIQHHnhAIpEYDIYDBw4oFIqR2FI0Go3P58PZaCRElQAMw5KTk5OSksLDwwsKCk6cOGE2m319fT/77DMajQYLVFZWdqeg69BAUdTX1zcyMtLhcJw5c2bz5s1SqRRBEIlEkpubGxMTA70Z3ASDwYDwk9lszs/Ph/QdoVAIzRiYTGZnZ6fNZktMTAR3vtVqhdax7iS+BgUFwWRwHBeJROnp6U6nU6/X19bWnjx5sqCgAGgVOBzO7Nmz169fHxYWRhBEYWHhY4895v6yKJVKNpsNDYUpFIrD4YiIiMjJyQFPJTANud7AYY0QyHrYsGHD4sWLrVbrqVOnTpw4AVIBlp6Pj8/UqVMFAgHsaUMMNdRjEAgECQkJTCYzKChIKBSCs4xEIi1atCgmJoZEIjU1NV2/fn2EjtuoqCjI8zp9+vRdiQKC9R8QEPDRRx/NmzevoqJi7ty5KSkpwGfS399/9uxZ8CF64ZibMWMGk8mUSqVHjx6VSqV2u53NZq9bt27RokX9/f21tbXuD2gymdrb24FJJzw8PDk5uba2Ft46cIf7+vouXrx48uTJHA4HwzCz2dzf3y+TydxZ8OPHj8+fPx9OnMDf197e3tbWtm/fvqqqKoIgUlJSxo0b99BDD0EgBkiCnnzyye7ubjfn73Q6r127dv78+Tlz5qAoqtFoWltbr127ZjQa6+vrLRYLmKbuLwiKoikpKWvWrBGLxXq93t/fHxhubTYbhmG+vr4vvfRSQkICfHjoRRjKby0UCuPi4kQiUVNTE/RQw3E8JiZm2rRp0Iz6008/HeEJD8xKHo9nt9srKytHHoK22WzQmohMJvv4+CxatGjevHkMBgNebqvV+uOPP9bX13tHwuQyELVaLY1GA4P18ccfnzVrllQq3bBhg0edvoxG49GjRzMzM/l8/sSJE8Vi8fXr1yGlrqamhkKhPPDAA5MmTQKZNplMLS0tO3bs6OzsdMf2vXLlSnNzc1BQELjwLRYLhUIJCAhISkpKT09fuHChSCRiMBjA6G40Gnfv3v3Pf/6zp6fH/UcAPpbt27c3NjbOnz/faDRevny5oaGhtLRUpVLZ7XZPU17BIqdSqeClhWM9hmESiSQ2NvbZZ58dP348mUyurq7esWPH0Aw+Q4k18HtDU2Gz2Wy32wMDA5988klfX1+CIAoKCkbS8dYFJpPJZrPBkBq5Y4ggiPz8/JaWFj6fDw4sgiBcLLoVFRX79+/32geCIAiDwQAPxt///vc5c+ZgGBYcHFxYWPj8888PDAx4etI/ceLEzJkzFy1aRKPRoqOj4bhisVgg3xDeRoIgrFZre3v7a6+9VlJS4ibJWHNz87333vvoo4/Gx8f7+fmx2Wwej0elUhcvXiwUCoFCVqVSyeXyxsbGzz//HLSsp8sCjKZdXV16vb6hoaG7uxt8F7cSCLoJ4PbGcRzDsIiICHBaTJo0KScnRywWEwTR1tb2zjvvNDc3Dz3+HcWaIAiTycRkMkUiUVpa2rx587Ra7bp168aOHYthWENDw7PPPut1ONAFFEUXLlwInS7KyspGOBpyw3uza9cuPz+/oKAgcNpA1KqxsfHvf/97W1vbSF7FkpISqVQKHYQ5HE5eXt7Ro0c7Ojq8a+A0MDDw6quv6nS6OXPmQDdAaKSJ3OBhslgsSqWyoqJi+/btEAJz8/jlcDiam5u3bt0KUfGsrCwejyeVSru7u00mE4lEUigUZWVlKpUKcsRHEiEWiUQKhQJ6MWo0Gu8ynBAEgWSB77///oknnkhISIiOjobzIo1Go1KpVqv12rVrr776amVl5bBka0O5XXx8fHbu3Dl58mSwz+h0Op1Oh2s/9NBDV69eHXk6BIlEeuKJJx5//HGtVjtv3ry70rkZwmZPPfXUhg0boOWS1WptaGj4+OOP//jjD68pFQHQtoLD4ej1eqPR6HXmw+ABmUxmUlJSdnZ2VlZWeHg4sKi1tbVdvHhRpVJVVFRUVFTAbunFGRcMJxKJBHY23DuGYXelKAZFURaLNXny5JCQEJlM1tPT09DQ4H63yNsO6Ovru23btkWLFlEoFDgcm0wmtVr9z3/+8+DBg4M7bg41zhB/o9PpTz/99DPPPMNms121WI2NjZs2bbp69erIS5sQBMEwbMGCBc8//3x7e/uWLVs83ceHGFYoFM6cOTMtLc3X1xcqvi5duuRp89l/G9AbRHvo7Vj27sqa/EUA55hYLEYQRKfTQfemkSgOFEW5XO748eMDAgLAF1leXt7T0zPyOpX/HxiGhYSE/PDDDy0tLTKZrLGx8c0334T8nrsw+g34+/u/++67W7ZsCQoKululK6P4N8MVQ/mf9ARdWuQvvcRfOv4oRjGKUYxiFKMYxShGMYpRjGIUoxjFKP6rgA7q3TqKkeD/nFvN5Un8r4pxpKSkyOXy0NDQcePGfffddyMpDP2PAKo06HQ6FEQjgxr03N0um25myf9vE2uoSL3pl1COHhISMmfOHGidWltbW1xcXF5e7l2NzN0Fm83+888/KRQKZGz39/e/++67e/fu9ZpL6N8JyLlLT0+fN29ee3v75cuXu7q6qFQqhBvv1suJ47iPj8+DDz44a9asH374Yd++fUMHuf+3EQHfVqapVGpSUtLGjRvT0tIcDkdHRwfU8N711qaeAhiM/Pz87HZ7WloaBOpCQkLef//90NDQV1555W4xF8PIrkKVuwUMwygUysKFC1etWiUWi319fdva2iQSid1ub2tr6+/v92LbcZEWub6IYZhYLD506FBERIRer+/u7h42A2KoxFQymcxkMoFLEqpu/mftjAiCoChKp9PvvffeJ554IiAgwG63azQai8WCYdh/A1c+hmFhYWEPPfRQWloamNSQc8xisbZs2eJwOF555RUv0pturY3FMIxKpQIhwd3KisEwjM1mr1ix4umnnwb6jvz8/P7+fh8fnylTpoSGhlZWVjY3N0NBMXKjteSww8KbPPgWyGTyRx99BIUgRUVF58+fH3ac24g1pALGxMQ899xzGRkZ0He1qKjo+vXrBQUF/f39kEd6V9KjXVcEXYLcIDYWCoUikUgulw8MDFgslmG34zvVuZBIpAULFmzdulUkEqnV6tLS0v7+/ra2NihGuivzR28ARvNIHUImfmlpqUKh4PP5JpNJoVCIxWLILVu/fv0///lPTws1bpVp1w8cDsdqtd6t7qBUKvWee+555JFHGAxGTU3Nvn37ioqKrFarSqUKDg4eP358WlraxYsXgREYFPDQA8Ia3jo3KOIG2uIHHnjAnSqK22trh8MB9H6Q48/hcAICAmbMmPHCCy9AXV1PT8/Jkyf379/f1dXlUSofTB3kGEEQHMeFQmFUVNT48eN5PB6GYZGRkREREQEBAXQ63Ww2FxUVffTRRxcvXvRi98QwbNy4ce+//76vr69Go/nmm2/y8vIwDPP39x8JyRhYNWKxGIhM09LSgoODoRDaZDK98cYbBw4ccHO2BEHodLrTp09//fXXiYmJV69edTgcs2bNysrKYjKZTCYzMTGxoKDAu3kigwj9oVYoKyvLbDafPHnyriTKBwcHA92UTCb78ssvgZIFSq0vXLig1WrT09MnT54skUgOHjzY19c3bBeBO/2Jx+OFhoYSBPH666/LZDJ3pnf75tA2m626uvrAgQNBQUFxcXHAU0GlUoF4DiRj3LhxGzZseP/997/66it3jFRQG1Qq1c/PLzMzUygUEgQxadIkPz+/6OhokGmQdeD6xnGcxWLNmjWrt7f30qVLQw9+2xVhsVivvvqqWCzW6XRvvfXWd999Z7fbGQyGwWCQy+VeHGhQFOXz+WvWrJk9e3ZqaiqXywVLBnQMlCy8++67Z8+ehdJdd0AQhNFo/Oqrr4BrncFgVFdXd3Z2Tp8+HWioQI94NE/XbF1cajDz9PT0oKAgMpl86NChkZQIIQhCo9EmT54M1XqlpaXFxcWQOAqWRnd3t16vp9Pps2fPHjt2rFQqPXXqlFwu9+4u3n77bQqFotFoPv/8cze/dXttDdVvV69e3bJlS3p6OovFotPpDAYjOTk5Li7Oz8+PQqEwGAwfH5/169f/+uuvQ5MZuzQ0iqILFizYvHlzQkIClKzBtYChwsWfIpfL+Xy+QCCAB+MyzjwCjuOrV69OT08nCOLo0aP79u0Dp4fBYEAQxAsOKhRFIyIifvnll6ioKBzHIRVYoVB0dHRYrVZ/f/+IiAgKhYLjeEBAgFwud19hW61WtVoN/zWbzcBWo1AopkyZEhAQ4O/v39XV5XW9CYIgcCiiUCg2m83f3//xxx8PCgrau3evTCbz7gSJoiibzeZyuQaDoamp6fPPP3cxMMKp1GKxqNXq1tZWqEtPTU09f/481C54ei0Gg7Fy5UoURR9++GH3F2Gooi+bzdba2gqExyCUVCoVtrNZs2Y9++yzEolEIBDweLyhKXZApikUSnR09BdffAEUeE6n02azyeVyYIytqampq6urra01mUzp6ekPPfQQvPqtra179uzxjvngkUceodFo3d3d77333uByKbvd7kVVC5VKffHFF+Pj4x0OR2tr608//VRUVFRVVYXjOJ/Pf+qpp8LCwux2u1QqBfp690cGu9NlBDscDq1WW15eThCERCJZvXr1kSNHoO7YoxVw2akoijocDsiYHzt2LIVCGT9+vEKhOHDggHcOcig0ZDKZRqPxzJkzwHY5uOgBKk46OztPnDiRm5sbFBQUFRV1J4r1ofHRRx9RKBSDwXD48GH3vzWMgw90iWvFwdhQKpU6nW7Dhg1Op9NgMID7fdhxgoODFyxYwGAwgJihrKzsyJEjZ8+e7ejoMBgM8B5DxeuLL74oEAgIgpBKpc8++2xra6sXTqK1a9fGxcUZDIa9e/d2dna6ip1wHPfCFQD6adasWQRB1NbWbt68uaioCN4NGo02adKkuXPnUqlUuVz++uuvd3Z2eqdc4eXncrmJiYkJCQmTJ08OCAgQCoUbN2787bff3n///f7+fjdHHvwxeIg9PT0nTpzo6urKyMiQy+Xd3d1Q8XTrgMP2MYJdNCgoqKurq6Ki4rake06nU6FQnD9/nkwmAx2uF64nHMcfeughgiD279/v0Vvtlt/aZUK4nBXh4eFcLhdBkLa2tiFohl1AUbSjoyMxMbGmpsZsNv/666+//PKLizzc9TESibR58+akpCRgGPr+++/z8/O92Ln8/f2feuop8Aft2bPHZrO5IjLgDWhsbAR+IzcHRFE0Ojqay+WaTKbPPvsM2FEIgsAwbPz48du2bRMKhRiG/fHHH6dPn/baFOZyufHx8cuXL09OThaJRD4+PnQ6HTi7nnjiiXnz5j3yyCPXr1/3wiyGDQGKskpLS7VabUdHx51e7+HdZzgeFBTkcDhOnjx5274lIC1Wq1Wr1VZVVSkUCjqdDtR+Hs38k08+gaOFXC4HF4KbX3dLrKHoFcdxcHr4+fmtW7cOyOJPnjzpzsVAYZSVlUE7rIMHDyoUipuWg0QijRs3buXKlUDTXVBQsGvXLi+8UWQyef369TweT6fTnThxwmg0cjgcHx+f6dOnz507NyAgoL+//5NPPrly5Yr7jPkEQcTExDidTpPJpFQqgcEIx/Hs7Owvv/wSKJS0Wu2HH37ohcyB8mOxWLNnz16zZg1QInV3d7e3twONIhSrBgcHHzlypKKi4rvvvtu/f7+nLw+GYUDAN3HixPr6+o6ODq9DMxQKhcfjVVZWXr9+/dYHBK3xIDKAoqhMJlMqlSEhIXw+3+l0uqMEAVQq9bHHHoPFefDBB1evXq1Sqaqqql5++eWenh4vCRX+5UM4HhYWBp0J+Hz+jBkzpk2bRhCESqUqKytzc09HUbSqqiotLa2qqsrpdLoSekDn4TgeERHx2WefARGtXC5/9dVXvdvNIyIi1q5diyBIf3+/0+nMzMwMDw+fOnVqXFwcg8HAcVwgEMyfP7+7u7uxsdF9I7u6urqrqysgIOCtt95qa2vTaDSxsbExMTEsFgvYPE6cOOEpWwM8M2jaIhQKQ0NDZTJZb29vUVFRWVmZ3W4fN27csmXLJk6cCExrTCYzNTV169atBQUFbW1tHi0L7FdA5uR0Ovv7+00mU29vr6fCjaKoQCCIjo4GzwYEHFxrCMvLZrNBkVmt1v7+fhqNlpKSkp6eDjRgbl5o/PjxMHhTU1Nra2t8fHxMTEx0dHRWVtbTTz99/PjxIWbubvAcAqGTJk2aMGHCmDFjmEym0+ns7Ox0/0GSSCSVShUfHw/Bz+bmZhqNBjRZUJS/efPm4OBgBEEMBsOnn35aW1vrhRGMYdiiRYvANNdqtRkZGQsXLgwNDYUWt2VlZcBKGhcXFx0d3d7e7mZOCEEQ9fX1LS0tISEhMTExoLnhpuADZrP5+++/97Qan0KhREZGfvjhhxqN5sqVK6dOnfr99991Oh00/MVxHJizGQxGYGAgsBgDD+oDDzzwxhtveGREEQSh1+vb29vDw8MDAgIWL17c1dXV19d3p0jWnYDjeGJiYnR0tEKh8PHxsVgsLqI96PsIrElSqVSlUkFTP6vVajAYOBxORUXFENO76TdTp051Op0dHR1z5szR6/W+vr4PPPCAv7//9OnT//nPfwJJ351mPrxYwzlarVYD1zxEjBgMBplM5vP57qfjwONBUfSpp56C1mxqtRr6KkFLAzqdDs783bt379y50zvCBgqFkpubSyKRBgYGlEolHNhramp27dpVVVWl1+sTEhL+9re/JSUlpaSkFBQUuJ/qpNPpNm/evHnz5lmzZonFYmBXM5vNmZmZXC5XrVZfu3bNI/nAMGzs2LFvv/12amrqtWvXGhsbGxoaTCbTYAd/UFBQfHy8Tqdrb28H8xQYj7zIZnE4HEql8sSJE3K5fMaMGSiKikQiLyqj/f39N27cKBKJBALBhAkT/Pz8gJiAIAgulxsbG8tgMPr6+qRSqV6vB8VEoVBIJBKPxxMIBLf16N+6bmQyOTExsbu7OzMzE1woAwMDL774Ip/Pv3DhAvTlOn36tPdijdyI5jscjrq6Oi6Xu3jxYqBv7O7udt9UgvYG0MbF19eXTCYrlUqr1cpkMqGDEXiFOjo66uvroSWmp7z24HiKjIy0WCyFhYUXL15ks9mQrAc0h2QyGcTFbrcDQbr7gxME0dHR8dxzzwUGBvr5+Wm1Wuj2m5ubSxBEcXGxOx6hwUBR9PHHH09LSwOHY19fH5xScBz39fXdsGHDvffeC4TqkMoCLmHQ0B5xWLrmb7PZFApFfX092CFAhuap+pg8eXJkZKROp6NSqUwmMzAwkEKhxMfHi8ViYBJUqVS7du2CYzpkFmVmZs6ZM+fChQvuv43h4eF+fn67du0a7BZ0OBwqlaqoqCg4OHho69FdI4REIkEeCHCdoChqNBo9DVZ1dXV9//33TCZz4sSJFotFr9dzuVyhUAieJjhP8Hi8559//qGHHjp58uTBgweBRNTNS7BYrPnz51OpVIPBkJ+ff+zYMUgkMBqNkBExe/bsl156ycfHp6Wl5dChQ556bcHn3d7e3tnZidxo5gIew6+//tpTk4lCoYSHh0MGUmRkZFhYmFqtjo2NfeGFF8aPHw+KGYQY+H8hjEehUFQq1eLFiwsKClQqlTsXQm9w6wDxO4vFCg8Pr6mp8YJsH0VRtVqtVqtVKhXYMEFBQQkJCRkZGUBqyuVyrVZraGjosWPHGhoatFptcnJydnZ2cHBwc3Pz0J0xXCCTycnJyS0tLbeGFel0+sSJE2Uy2Z3sGYC72hq5kSoO/nyI1Pz6668erYvJZLp+/frTTz993333zZ49OyIiAt51giDMZvPAwIDNZmOz2ZDiGBcX9+CDD3777bfffPONXC4fVrhRFA0MDFy0aJHVam1qamppabHZbNAzUiAQ5ObmQot5EolUX1//j3/8o7y83GtiKpcXPDk5GUGQgYGBoqIiT9UnjUarr6+fNGkSiqLh4eE//fQTGBjIvybL2+12YForLS0Fhr6IiIhr16656VeFlATnjXadIpFoxYoV/v7+0E7SUwI0yDABFkI4MTOZzPDwcNB0cCEajZaUlJSYmAic8MBhWVxc/Mcff7j55uM4bjaby8vLb/o8m83+6quvgoODz507N/SCDy/W4LQmk8l0Oj08PBwsV4PBsHPnTk/DaRiGQb5LaWlpZmYmiqIqlaqzs7Ourq64uLinp0elUmVnZ69evRr46Nls9qpVq8hk8jfffNPV1eXOogDpY3h4+LPPPtvb2+vv7w/NUWG3bWtrKyoq+uKLL+rq6rxm9XSByWQCeWxzc7P7xpgLWq32ypUrK1asYDAYkDjq+hO4EZRKZW1tbWFh4a5du7q7u10hw6qqKjeTPMHLBp5ZFEVDQkIeffTR5cuXKxSKnp6e5uZmT7U1QRBFRUVCofD++++PjIzEMEwgEFit1r6+PrlcXl9fT6VSw8PDIyMjeTwepN9IpdK8vLwjR460t7e7s+AQzJ4yZUpUVNTAwMDp06c1Gg2Hw9m8efOKFSskEklDQ8MjjzwyNMO/W0dGEokkFAojIyOfeuqpwMBADMOam5v//PNPT7ddOF9iGNbd3Z2Xl1dUVAQ5FdXV1WDhIAhSV1dXUFAQHR29efPmsLAwX1/f7Ozs6upqd+jE9Xp9dXX1zJkzqVSqj4+P0+kE/We1WktLS3fv3n3mzJmBgQEwnEYo0wiCZGRk4DhOEMSxY8e8cNoQBJGXl6fX67ds2ZKQkAAnZgi/nzp16vDhwwUFBeBZvylkCPnidxrW5VVwqXygbff19X344YdXrFhBo9EuX7588OBBLyLnBEEMDAycOHGip6fH398fHOEIgkB3kcbGRp1OB3nYQqEQeFmB9NVsNru/RKGhoZGRkZMnT87OzoYvwptvs9muX7/+0EMPuZnHNxQwDONyucuXL//999/7+vr0en1vb+/9999Po9G8GxCy8+DAQaPRyGQy5L6hg4Dj+KZNm7q7u5ubm0+ePAmVI8OOTKFQ0tPTDx8+3NLS0tjYWFNTc/369W+++WbSpElwPPLi4D/EXRw9etRms6lUqgkTJng3MtwphUJhMplUKhXCLu4M5U4ZL1gFFAqFRqP5+vpu3LixuLi4qanp/fff53K5I1kK6FdEpVLpdDqkwUG0bvDkXY/SC2I+JpM5efLkQ4cODQwMaLVavV4PG9djjz0GvfzuAlAU9fPzO3z4sFqtNplMAwMDH3/8MbQYHcmYLrMPfr71AxEREfv37z9x4kRZWRl45t0cmUwmQybdX8p0SKPRoDFAbW0t8IX+FwIWmUwmi0SiVatWAT05bAv/6akNA7DKeDyeSCTy8/PjcDgQkHLz624ZIdDdC+yzoqKi9957z1OrevBoyI3D0OA8k1vR2dn5+eef02i0p556yn3vOLixvJiYp/Dx8YGAqEwm+/dc0TvA8jKZzCtXrmg0Gq1We7fqI/9SQHbrX1hsCmK9YMGC06dPP/PMMyPcv+50iVt1tiu1wN/f/+5e7q5gyZIlBoPBaDTu378fGnb9dwKyAkUiEZvNHmUguRlgBd7FdbnVCLv1A2AN/zfU0t4EFEVnzZql1+u1Wu0rr7ziUd+6fzNgARkMxmBPyyhGMYpRjGIUoxjFKEYxilGMYhT/V+GBq87TfPNReAFwXEAMBYplbq34HMWwcEusoZAuLCysrKxMq9XeXXrC/36g7pHPjvwqVCo1JyfnwQcfnDFjBmRBQK7FY4891tDQcFcm8O+5l7sLiJXSaDQmkxkWFgbJg9XV1a2trf39/VCAc9NXhne4ksnkdevW3X///Vartaam5osvvmhqavJasqE6bXAB3G2XeLBXGxkBR7Ir1XgkuU13+uLdFRHgBV22bJlLplEUpdFoycnJOTk5kGfr3ciQUCASiSZPnnzfffeJRKLz5897QTT3HwEIdHR09PTp08VicWJiYmBgIFDT7Nmz5+jRo5BhelNC3zBijaKov7//mjVrYmNjnU5nXV2dTqfzOsoI2RpQlIogCJVKhSoYtVpNJpOhtJHJZI4bN04gEERERECq3ZEjR4CFx322K6B82LZt24wZMzgcDog1lOfs2bPn3XffHTqt0c17gco3aBgOKeNeJ7uiN5jypFKpUqmExD0ajUaj0QiCWLBgwc8//+xd2hrE0aKjo+fOnTt79uz4+Hig+GCxWN99911LS8tIYumuYNlfZCZB4uv8+fPnzp0LlYFMJpNOpwNBZHNzs1qttlqtHmtrFEVzc3ODg4MtFkt5efmBAwf0ev3QuRxDAJKeoehj3Lhxa9asodPpQFAWEhICxacCgQA6q8MlbDZbamrqqVOnPv/8c7Va7Y7coCgaHR39+++/R0ZGDo5QoigaFBT08ssvL126dOnSpXV1dcPWJdzpA1DYsmLFCugprNfrFQpFS0tLQUEBpOd7ujJQdyOVSvfv39/T09PT01NcXMzj8V5//fXMzMzExMQpU6YcPHjQizVHUZTFYmVkZCxdujQ6OppMJkO517p160JCQl5++WUv2IWQG+23ExMTQ0JC9Hr9xYsXFQrF3RVuEokkkUief/75xYsX02i0/v5+qVQqEomYTCaCIFqt1mazgUzfetFhxJrL5S5atAhF0YsXL7799tvt7e12u51Go3lHBAyMmiiKAnFRQEBAQEAAFJJRqVQSiWS325VKZWdnp1QqBUpcgUDQ0dFRXl5+pxu4FTiOr127Njw8fDDvI1g+cPWYmJiCgoL77rsvPz//TgMCcQfUIw/+PWzocXFxq1evnjFjBo7jFotFJpMBe2pmZuZ7773nIpHyCE6n02g01tbWNjY2QhGnTqfT6XSgnHg8nqcDIjesUolEsmLFitjYWCqVCslDsBVMmTJl/fr1b775phcEqiQSKSoq6oUXXvDz82tqasIwrLCwELKr78rRi0QiJSUlPfvss7m5uUBPQBBEdXV1aGgoiUTq7u7+6aefSktL7yQSQ4k1hmHp6enBwcHt7e2fffZZTU0NQRCQHg2VWoPfTtcPt21z4QJ8DN51MpmM4ziO41Cf29fX99FHH504cUKhUICRQKPRQkND/fz8IPffnfUikUjZ2dkbNmwgk8kIggCV0fnz5zs6OjIzMxMSEiC/USAQ/PjjjwkJCXdij6bT6bdm2YOxGx8fv2jRojFjxigUitbWVsgGptPpqampEyZMWLt27bvvvuvdowXuAdAXcK2xY8eSyWSbzVZSUuKdIiSTycuXL09JSaHRaA6HA9LlofKIzWYvWbLkypUrR48e9bQMAkXRyZMnu2reZs6cOXny5I6OjoaGhmvXrimVypEIN4qiEolk27ZtWVlZFApFp9OVlJS0tbV1dHTweLy6urpPP/20rKxsCGqkocSayWQuWLCAw+GcPHmypKTEVS4KmT34DfD5fKvVqtFoQKECJ9UQdwVH/uDgYB8fHxRFBwYGWlpampqa9u7de+nSpcFmhs1mq62tbWtr8/f3Z7FYwzLpQ7LhQw89BCl1Tqezp6fn5ZdfvnLlilqt5nA4W7ZsWbduHYvFQlFULBY/8sgjH3300W3HhI3lpsFJJFJCQsL06dN9fHwuXbokk8nq6+v7+vosFgvYfLGxsfHx8VQq1eujGGwscK0pU6aIRCKHw1FfX9/a2urdgFwud8GCBbAgOp2utLS0tbWVSqWmpKTEx8f7+flt3bq1urq6paXFo9eGRqMBKY9Wq+3q6jIYDFFRUTNmzODz+RUVFe+88w6Qqnk3ZxKJdM8998ycOZNMJptMpt9//z0vL89gMPB4PA6HU1JSUl9fPzQj11Bizefz4XU8efKky+SAh83j8ZKSkoBaICIiQqvV9vb2njhxoqamhkKhDHEggxNMSEhIbGwsm83WaDTV1dU2m625ubmvr891icGbgMPh4HK5btIVcLncKVOmgKfFYDAcO3bs9OnToDw0Gs22bdvEYvG9994LLN0bN27cu3fvbZkrbru7cTicpKQkgUBQUVFx7tw5lUql1+vBYKBSqb29vWw221OehjuBwWBMnTqVSqVqNJozZ854d8YFhomAgACw3RUKxcDAwNmzZ0Fn+/r6SiSSmJiYDz/8cO3atUOYIjdRN6EoyuPxQkJCrFZrSUnJ9u3btVptQkJCVlbWuHHjxGLxBx980NDQ8MwzzygUCi+mjaJoYGAgcGW1tbX98ssv1dXVEokkJCTk0qVLFRUVw+4GQ/WO4XA4fD7fYrFAAYHrTzweLycn5+GHHwYJhvRRPp/f1tbW2to6dLEq7K25ubkBAQE4jjOZTKD1RlF03rx5dXV1KpVKrVZ3d3eDyscwDEhWETfcfCiKTp061c/PD14Mi8XyzTffANkfPBKFQrFx48asrCx/f39w8vB4PDcp1qEckM1md3d3Hzt2DJjQXA/bbrezWCwMw6AJiTsDDn0jQLuBIIjRaKysrPSu4QuGYWlpaVDwBueW8+fPV1dXm0ymnp4eiURy3333cTicqVOnPvbYY5988smdDrs3uUdhegKBwGg0HjlypLq62m63t7a2/vHHHyKRaOrUqY8++mhmZubGjRvfeecdLw7QDofjyJEjq1atgpMicILCC9PY2KhUKofdDIfKnxYIBBwOx2AwMBgMOp1OIpGAmyc1NXXDhg2BgYEKheLXX3/ds2dPXl7e4cOHoXPFsO6F1NTUBQsWgKcPGDAMBoPBYIDt8qmnnlqxYsXixYvDw8NFIhGdTvf3958yZYo7RWwMBuPVV1919Rb6/vvv6+vrB+tdgiC0Wu21a9fgvziOx8fH33YocLcNnjbcO0EQFRUVrlfFNTKZTM7IyACraeTamkwm33///cHBwaAyvChrR24Qgubm5lKpVBRFHQ5HV1dXbW2tUqmEymjXeYnJZD7zzDNRUVF3ct3eesYIDw+HHO6SkhKLxQLcDBaLpaen57fffvv2229RFF2yZIl3BRawyN9++213dzeGYQsXLrzvvvsiIiLkcrmb/vuhaNt7e3sbGxsJgoBCFTqdzuPxFi1aNGPGDD8/vyNHjoDc2O12V+eAYcWaQqFkZWVBOR0QHMJ5rqWlpb6+3uFwQLeagIAAPp9PEERqauqsWbOgPdewNwMtXeBnnU730Ucf3coLRRCEq4idIAgKhXLboex2+01+TBaLlZSUZDabW1tbgVLeNQiKohkZGWPGjCEI4tKlSyN0BUDlNpVKNRqNdru9t7cXmPM9BYqiiYmJ48aNA4+Q3W6Hngc2mw00aEtLy3fffQfVjT4+PsuXL3/zzTfdUa4EQcBmq9FopFLpTStstVrr6+vBleTr66tWq72obweKPR8fn4CAgNDQUAaDUVRUlJ+fr9Vq3fKGDfG3rq6uV199VSQSgcXMZrPT0tKmTJni7+9fWlr61ltvuRzJcCBzM5KH47jVaiWRSBqNprKy8pdffmlubtbpdNDBCTxx4GkJDAxcvXp1aGio0+m8evWqVCodei8GtYQgiNPpLCgoGBgYuHU+IDTws8PhKCkpue1Q6I3GIK5vBQUFpaamarVaf39/4N9QqVTAtAQ98mg02tWrV+vr62/arz16qEDXS6PRDAaDSqUik8nwIAcXELk5IJlMnjx5sisaBepJp9O5iJttNtvZs2e1Wi0U16WnpwNDlTvjq1QquVwOLIS3/lUgEDAYDJlMxmKx3L/3m6BQKIqKirKzs1ksFng/3ZRpZGixBkZq4CqHSmAKhUImk7u6ul577TWlUgmtIWCD5nK5txWjm8Bms3k8nlwut9vtzc3N+/btq62tdXXAAEB5JoIgWq02PDw8ISEBHsawFPmwM8IIeXl5tyoecJmPHTsW/ms0Gvv6+m47GvGvgX0ymTxz5sykpKTOzs758+fLZDI6nV5ZWdnZ2alUKsPDw6dMmTIwMLB79+6b2qu5+RhgGeEgAYTtEAIDv+eECROAvhD2lpuW604DMpnMKVOmgPMUpiEQCOC7rqO50WjU6/XA9SGRSFyO7aFBEERtbW1HR0djY+OtdYAoimZnZ1OpVGiW587t3zoCxBdDQkJMJpNMJouIiBgzZoyfn5+bTXmGEmvwQvD5fKBxMhqN/f39Fy5caGxsBNJvUKs8Hi8sLMzHx+fChQvDPkUgXy0vL//jjz/Ky8tbWlpu65B2ObmQGy7kjo6OYQePj493xXKrq6tvy5IfGRkZGhqKIIjT6byTsrn1WxKJZMKECcDh1NPTExAQgCDI3LlzrVZrR0fHggUL/P39gZlk2NEGA/hSJBJJWFiYn58fi8VSqVQoisbHx6ekpPD5fL1eHxYWJpFIUlJSSktLm5qaurq6zGazO7EwKpV6k7nc3t6uVCoHnzRoNBrsXbDluh9i6+vrO3bsmFQqBWttsJOEzWbfe++9CILU1NR42lQSGeT/nTp1KnTy7u7uhmhdXFycXC53J447lFjDSzNx4kSj0XjhwgUUReVyeW1tbWVlJRiXFAplzJgxU6ZMIZFIP//8szssQU6ns7a2tq6u7ty5c0D2M0Scb+rUqTExMQiC9PT0DMvqBFEo1/sQEhJyUwgDfDubNm1iMpkEQRiNxieeeGJo/7rr6ziOt7a2crnc6urqsrIyqVRKp9ODg4Nzc3OXLFni4+MDZHPAYTlYksAFcacbDA0N3bJlS2JiYmhoKBzp4NgtEonguIwgCI/Hw3E8ODiYyWRardbu7m53MggIggAb2mVK6XS648ePD95MSCTSjBkzYDXsdvtNfx168N7e3gMHDkDbQVc+GcTpli5d6uvra7PZfvrpJ4VC4alhDUrk0UcfnT59ukAgaG1tbW1tZTKZAoFg2rRpqampR48eraurA2PBm3AMvM3QqxOO0hA3AZlmsVhRUVFPP/20Xq8/d+6cTCZzZ1GgNwWHwzEajUN3RkxKSvr666/ZbLbdbt++fbs7Hi4XewmGYdOnT8/LyxusRchk8rx58+bOnQtx0JaWlra2tiEmQNzIS0EQRKVS5efn19fX63S65uZmuVyOomhHR8fYsWPB8tPpdBC9wwb1eB7asMZxfOrUqQsXLuTxeLCJsVismJgYNpsN/QEZDAZQZzmdzr6+PpVK1dPTI5fL3RQU2L5BYTscjvz8/LKyMtd3MQxLSUl54403wGzTaDS///67+25EuGUIlYPLSCgUIggSFBT0wAMPkEiktra2y5cvexGWgmh/VlZWTEwMnDt5PB6Xy6XRaHw+3263Z2RkdHZ2/vrrr6dPn75TUGaYnBBw1gqFwsDAQCBydTgcQJ2amZm5bNkyJpN59OjRU6dOudmHBUXRsWPHhoSEnDlz5k5+KzAVzp8/D8fQysrKw4cPuzM48FaCHTJnzpyYmBg4wEEMaPz48Vu3buXz+fDJ7du3Q4/GIeCysDUaTWtrK3C1qdVq0EzAMCGTyahU6sDAwKlTp5RKpYue1NUv706DA10b9AQEp7JKpQoKChKLxcBKhSCIw+Gw2WwtLS3Hjx8vKiqqrKx0U6HCPV66dCklJYXFYkG7NrCtYZtNT0/fs2cP+O8tFsvOnTvdpH50rYzNZoPXANi5NBoNnU739fWNiopyOByHDx8ednnvhIGBAS6XS6VSoZwCVBuci5xOZ0BAAHC0KpVKCEvfOsIwvB9AhhkaGjpv3jyJRAKE+Gw2Oysr65FHHoGoz/nz5wdbbEODTqdHRUUFBgY++eST0B0LHZRaDUQtzzzzzPXr16GTmEKheP75590MMapUKmD5RlE0ICBgx44d48aNEwqFEolk+fLlP/zwQ1hYGIIgkGH7+++/DzHnmzy4kF4nlUpdtjiJRGKz2b29vefPnz906NCePXuuX79+k6U+9JrY7fbu7m4ImDkcDl9fX4hmQ88GcANrtdqKiooffvjh6NGjV69e1el07mfJ2e32/fv3l5eXm81mDMNycnI2btyYkZExY8aM3bt3//777yDTRqNx+/btd0oiGAJw9HI4HHa7HU6HZrNZIpEgCKJQKH788UfvQkgOh6Ojo+Onn34CA9WlQSCrGSSQyWTyeLwhpGIYbQ1NXe+9997U1NTp06cXFBQoFAo/P7+kpCQEQQ4fPvzdd995lNei1+vLy8tXrFixcuXK0NDQL774oq2tzWKxMBiMyZMn33PPPRMnTmQymUBz2t3d/fDDD1++fNnNB6lUKr/66qs333wTViEjI+PYsWOgQUUiEZ/PB2E1GAyvv/760Jznt17RYDBAsiGDwXA6ndDHSCqVHj9+XCaTAQM31Gu57OkhjBCYSV9fX1FRERjTLntDqVTK5XKZTFZcXHzlypWmpqb+/n69Xm+z2TzyiBME0dzcvHXr1g8//DA+Pl4gEDz44IMrV66ETHHoYqzVat95551du3a57zsbYq3sdrvZbDYYDA0NDbf6s90fzWq1fvrpp0qlcsmSJfHx8cDjDC4KOO8hCNLa2gp+C09dqAhyI0z6888/KxQKtVotl8s7OjqamprOnj27efNmL4jLIH7W3d0NriWpVNrd3Q1VAlqtFqwIs9nc0tKybds2X19fT8eXSCTgAyJutKQAjeL6WaFQvPXWW14Qb4Ilw+Fw/P394+Li5s2bt2jRoqSkJBaLheM4aBQWi8Xn8318fFwedOQWxe/6JfhMg4ODs7OzV6xYsXbt2pUrV6anp/v7+3O5XD6fD7vwTWdQT+dMo9HGjx9/+fJlcJJC6xKr1WoymUpKShYuXHi3mCZRFGUwGH//+9+bmpq+/PLLEZJIoTea3o8ZM2bnzp1yuVylUgGHYHd3d35+flpaGkS+b/91dy5ApVLj4uImT56clJREoVAuXbp04cIFyL32dLpgrL/zzjvTp0+HuAMktkONiclkam9v371794kTJ7zLx0dRdM6cOd999x2kB6L/mjWlVqv/+c9/7ty50x0X+60jk8lkX1/fmJiYhIQEMEsuXrw4uLiBRqONGTPG4XAMDAxALxhP53/XAdOOjIxcuXLlxIkTQ0JCcBzX6XSnT5/evn17T0/PyOnrXWAwGM8888zChQvPnz//+uuvj7wECbnhYIHWLlwuF84hra2tKpVqiJl7/Jp6o/P/FRiGcTic3Nzce++919/fH6Stq6urpKTk1KlTcrkcIt5eXwVF0ZCQkL/97W/z5s2DGJvT6ZRKpbW1tc899xzkkXoxOBTVxcbGTpkyBcfx4uLi6upqyJV1nSxJJFJaWhp4grVarRedN/46wP7gynXxiEfdTTAYjPvuu2/WrFnHjh37/fffPe1odRfhMSfiyCfqdDrVavXPP//8888/j3Co24IgiPb29o0bN97dYSGdOi0tLSAggMfj9fX1FRYWDnYMw6VbW1sNBgMc0YZwWv/74Trhue9L8RTQxXlgYADSZv6Dr/R/O333fxXgRAhaGTwAt/0Y+j+QtOBugclkUigUi8UybLLDKEYxilGMYhSjGMUoRjGKUXgFFEWnT58OJU//6bmM4n8k/ot65GAYFh0dvWXLlj179qhUKlc5/v8p4XbVEwBZxeCOlXfxKlAcHR4e/lc0uPpvwFC3hA7qx+pqMwysIJAeDgHquzIPBoNx//33P/744zabjclkXr58uaqqau/evcCrdFecZegNIHfgS7grgEt4sSwMBiMmJoZMJms0GofDMXny5JycHJvNdvHixVOnTkml0rtFAwnlpGvWrElOTr569eqLL77oZibZ/yAMk2+N3Ii+RkRErF27NisrC+pqW1pajhw5Ul9fP3JeYKinWLVq1X333QdVMH19fcePH+/t7XU1oIcIqqfPFfIKIAoIfKQPPfRQeno6lUrdvn370aNHR/5OupQrdML18fExGAwQlXA/6gEjjBs3LikpCUVRk8mk0+mCg4OlUimGYXFxcZDod7fEmkQipaSkQEpZcXHx3Y3wu0oKbqqa+zdjeGpJaHi+bt26uXPnMplMjUYDecb333//1atXT506NTAwMBJOQajRWLRoEUEQH3/88eXLl00mEyQnwYMcNnH5toBYN5lMhsdGoVAkEklaWlp6errNZktKSvrjjz9GSKhFo9FCQkJEIlFAQMDYsWMTExOBd3n37t3Hjh3zaLTQ0NA5c+ZkZGQ0NzdfvHixrq6utLSURCJFR0dPmzZt0qRJjY2N3lH73Tptf3//FStW+Pr6/vrrrwcOHLgrLT0hMZrH402aNGns2LEUCuXChQvXrl1TqVQjXGQ6nb5mzRoGg/Hll1+6rync4reOiopKSkqy2Wyw3C0tLSKRKDIycvXq1SKR6Lfffuvp6fEuwQBy21etWhUdHb179+7Dhw/b7XZYo5vsBPfFGhQGpF9yuVytVgslxhwOJy4ujs1mq9VqIK/xYsLIje2Ly+Xm5OTExsYCebFIJIL05bi4uOjoaCaT6X6qJ5VK3bhx47x581paWn755ZcrV664QnQ9PT3AWpaamtrd3T1ysSaTyY888khUVJTRaPz555/vClMP5P1OmjRp/vz506ZNA/qh5cuX79q16+uvv/ai7msw6HT6zJkzx40bd/DgQfeJJdxqDm0yma5cuaLVaq9evdrV1WWxWKhU6vjx459//vk1a9Y0NjZKpVLvrFUMwzIyMlJSUvr7+7/++mtQz2BMk8lk73KSXEkaQKxjt9sdDgeNRouMjJRIJEDncOnSJa95ksLDw++7774VK1bw+fyurq5Lly4VFBQEBQVJJBIOhwOsu/v27XOTswZK93Jyclgs1m+//Zafnz84Mc1oNF69ejUoKIjNZo88wwTDsKysrEcffZRGo7W2tt62itlT4DgukUjWrl27ePHiiIgIoLZCEEQikdxzzz2HDx92v8TkVhAEYbFYoOReKBTeNbGGnO6mpiar1apWqwcGBuD9hs0dcvMzMjLOnj3r3byZTObatWs5HM6hQ4cG5/UDk47Xtg2UJA2uo2axWIsWLYKi1/r6+o6ODi+GxXF83bp1zz33nEQiodFoFovl8uXL3377rclkYjKZJBJp48aNcKr28/OTyWRuVsFNmjRJIBCUlJQcPHjwpmRLgiD0er1cLoeaOvRfa7w9XRyBQPDpp5+y2WyDwbBt27ahCyncAdAerF69euXKlcHBwcDUhdywXaEcZISeFovFAnRioaGh5eXlbn5reG0NtOrt7e3AMQxTDwsL+9vf/iYUCoH7y7ucXcggHTt2rNPpHHyAc1W5ejrgYAzWQyiKhoaGjh07FujRzp0758Xmi6LoK6+88vzzz+M4DrVSv//++9NPP20ymchkssPhAGYMHMftdruroGPYYWEbkcvlv/zyy21L94G+8VYvp6frQyaTX3jhhfDwcARBzp49e+bMmbuSmIqiqI+PD4fDGSzBUMre2dk5MDCAjDiZ2cfHh0ajAYmFmxherMGLZ7FYoDZEKBRGREQ88sgj0dHRMpnsnXfeOXXqlHebI5lMfvHFF/l8fk1NjasoGo56KIrexbYmFArlySef9PHxgWLbH3/80dPNF0XRJUuWPP/881Qq1W63NzU1bdmyJT8/H0pfEQQJDw/PyspiMpkwbaAFcwdUKnXs2LF9fX35+fm3nRVU9FAolBE6JX19fZcsWYLjeHt7+9tvvz0EObT7AEeQSqVqb28HjkIXT4tCoTh69CgUBI7kQg6Ho6ysLD09PTo62v3Xwy3bmkKhiMXi1NTUjIwMf39/BoMRFBTU1dX19ttvnzp1yuv8XT8/vwkTJpBIpH379kElBbjkoJDxbrmWURTNzMxcsmQJ2Kb79u3r7e31aAQMw5YsWbJv3z6Q6b179/79739XqVQuB6hIJIKSCMjQ9/HxmTt3bk9Pz7BmJawtiqK1tbVDHK1As4A69G5NYL8SCoVWq/Xw4cNdXV13y/VGEIRUKjUajcBQgyCI3W7XaDQnTpzIy8vz7nR00/hHjhx59NFHx44di+O4m8rOLbHmcDjLly9/8MEHRSKRa58tKiqqqanx+hCDomh4eLhAIHA4HMDbCR4GYLiTSqWDW2R4dwmASCT67rvvoB9NX1/f+++/79Hmi+P40qVLd+7cCTbGjh07XnnlFRd7BHigNmzYkJ2dHRISAtSBbDZ77NixfD5fo9EMuz50Oh2ofm/7SWivAU1wGhsbR9KjMT4+HsdxtVrd2toKNTJQVTCS5QXbOjY2duzYsWw2G8dxgiBMJlNVVdW+ffvcpzQZAlCZYbFYeDwenU6/m2JNo9FSUlJEIhGKolqt1mw28/n88PDwl156CRrKeDd7X19fKpUKrHAg0+Hh4cnJyX19fUwmUyaTabVaYJhFvDW1qVTqu+++C6VlJpPppZde8rSKccGCBd9++y20bnrooYd+++03mA+QY/j6+j766KMPPvigUCiEWlcI/URGRs6fP//TTz8denD48ODSBBeFAIPB8PHxAZaP+fPn4zh+6NCh4uJi1yHHo3UApi8w7caPH9/X1zcwMKDVavv7+6GVkUejAcBnunbt2tWrVwOjHTgYOjs7q6urYUMYfF70WsShAQaVSoWznDtfGT4cQxCESqXav39/VVWVWq2+fPlyQEBATk7O7Nmz58yZw+fzH330US/IXjEMS0xMRFHUYrEIBAKBQBAcHPz888+z2eyrV692dnbW19c3NDTgOA4kfV4sColE2rRp07JlyyBCeeHChaG5QW47yW+++Qb8J42NjYcOHQI2TQaDkZqaunDhwpycnICAAGCxcYXljUZjXl6em94hh8PBYDBmzpxZWFjY3d0NrRemTJmybNmyyMhIg8FgNpujo6OBPGnChAkXL14sKCjo7+/3aB/DMMzPz0+v11dVVXV0dCQmJqalpREEUVlZ+euvv9bV1Xm666IoyuPxHn/88UceeYTP58MpH4qsof2NSCTSaDTw7Fys++Dg8vRCLBaLxWJ1d3fDYd2du75ZrF0FS4PfM6PRWFBQcOXKFZvNZjKZamtrr1271tTUtGjRIjabPWHChAsXLnhhRYESxXF8yZIlGRkZc+bM8ff37+npgb0bGLVdLQ89tUZQFE1OTt6yZQsMIpVKX3vtNU8DxQwGA4p8EQTBMCwgIIBGo23ZsmXWrFlMJhNOeHASAC5T4NH7+9//XlhY6OoZMjTAJzNx4sQlS5ZcvXoVw7Dly5dHRkb6+PhYrdaKigqBQMBisfR6PYvFmjhxYnR0NIVC+fnnnz3qtEaj0RgMRk1NzR9//GEymYA7prOzE1qOfP/9921tbe4fo2EDz8zMfPjhh3k8HogaVElCVwaxWLxq1arz589XVFQALQ50e7rJR+km2Gw2BNfAyHHnK/8i1rAbojc4AuGBQRwbfE8u2VIqlbt3766oqNiwYcOCBQsqKytlMpmnexn0O4N+U+ASgn6EJSUlkZGRs2bNSkpKAkKqnp4ej0ZGEIROp69duxYMJ4vFcujQoaqqKk8HiY2NdRHdRkdHl5WVuQ5GDodDpVJVVlaq1WrIr7DZbJWVlStWrAARcfMB6HQ6vV7PZrPvuecejUbD5/NpNBo0iLp69arNZgN7z9/ff9GiRUDl6HA4WCwWnMzcuQSKolwuV61W19TUdHZ2Aj3LiRMnIL6bkJAQFhYGVDJujgY0eatWreJyueDbtVgsEKSjUqlcLnfcuHHA5gF7EbAgeOcGIAiio6MDyHTcF7B/EWvwFZBIJH9//6ioKAqFUl5eDlzUN80GNGh1dbVOp4uOjg4JCfHURCMIIi8v7/7772exWDQaDWg3qqqqLl26FBQUlJiYmJWVpVQqz507R3ieJ0gikXJzc1euXAmn287Ozry8PC8sSGjSCjQ0CILADwRBGI3Go0eP7t27t7u7OzMzc8qUKfDmb926FYqu3b+EzWbr7u4mkUiBgYFCobCwsPDIkSMKhUKn04FNqVKpFApFYmIibDXd3d1Akg+0bO4Ax/Hly5cnJCR0dnaiKOrKHfD394+OjnZ1PXR/zhQKJT4+HrxhOI4rlUq73R4eHs5kMiHrQS6XHz58uKCgABxckGeLeGteW63WlpaWsWPHuk/q9y9iDetIJpNnz569dOnSvr4+aPt5py/7+PiAh47JZHoqNE6ns7GxsaenBywzm82mUqlYLNYjjzwCDnLwfMlkMrgZ91cEx/GsrKwPPvjApaovXbrU19fnhYOstbX1qaeeSktLmzt3LhimEomkvr7+nXfe6enpgQj/kiVLoCNeV1eXF8QgQOYCjI9qtbqpqcloNAKhMJ1OBysoISEhJyfHz8+vs7Pz7NmzAwMDMpnMzYgShEsWL14sEoliYmJKS0sdDgebzZ48efLmzZtDQ0NPnDjR3Nzs/qsIZnpAQEBtbS2Xy1WpVLCZCIVCcIB2dnbu2rXrzz//dBHYInegtnIf7e3tqamp7nNx3ebICCm/QEorkUhqa2tv/QyKor6+vs899xyTybx27VpFRYUX2QU6ne7PP//08fERi8XQTCwqKgoWAsfxmpqao0ePnjx50qPcV6hFeOONNwIDAyHv2WQyWSwWICYEl5b7M3Q6nbt3796/f/+mTZtcBhiYAcQNGqc1a9ZQKBS73f7zzz97kbgMDiy73c5gMNLT04Hq3Gq1hoSEzJo1y+l0crlcDMOYTCZk9pWUlIBf1f014XA40H4lPj4+Ozt73LhxkIeDYVh3d/fHH3/skXcI/PTJycm+vr5WqzU2NjYoKMjX1xc8hh0dHZs2bSouLr6J++am05qngGsB2607uFms7Xa7wWBoaWlpb29PT09fs2aNQqGora2FZFEEQWCJJ0yY8PLLL4eEhDQ3NwMLoBf7C4Q2nE7nhAkT1Gp1T0+PSCTq7+/XaDR9fX1nzpyRSqUenURRFKVSqatXr46NjYXYtcPhaG9vv379OrTI9uLI4nA4bmqb6XoxUBSNiYkJCgpCUVSn0507d86LJAKCIIqLi4uLizMzM2fNmhUUFFRdXc3hcMaMGQPJPR0dHZWVlWVlZQ0NDdCtBlhx3b8EjUYzGo1MJlMikSxcuBBa6Fqt1rNnz7755pt1dXUeveokEikgICAkJCQyMpLD4QCFKRh7HR0djz/++LVr127rXR6JDxv4ygb3Xhsat9HWDoejqqpq//79JBIpMjLyyy+/HBgYuH79ulQqFYvFfn5+oaGhgYGBTCazvr7+lVde8U5VIzdOA19//fUPP/yg0+lMJhO484A4GTSip2vB4XBmzpzJZrNRFHU4HEql8tChQ4WFhb29vd4NOARwHF+zZg0cz2Uymdf5+Eql8h//+Mfbb789a9assLAwHMflcjmGYY2NjXv27KmoqOju7jYYDIPn79FdKJXKysrKlJQUNpsNhPnHjx/fvn17aWmp0Wj04sihVCp5PF5gYCCEhJ1Op9lsPnPmzMsvv9zQ0HDXOdAQBNHpdCiKutlBE7mtWMNx8M8//6ysrFy/fv0999wTHx+flJQEPQIRBBkYGGhqavrjjz/y8vKG7b41BOAE3dvbe9Nu5d1oADKZDFyPZrO5ra3to48++uOPPwYz5d0tgO07ZswYOGc3NDS46dG7FQRBdHV1Pfnkk1OmTPH19TWbzQMDA2q1uqqqCjqJ3bYJDuLeWkFw+5lnnomJiRGLxZATUlJS4ibN/q1wOBxarbanpwfCltCc9+OPP963bx80vvBizGFx/fr1qVOnuq897xiOsdlsXV1dr7/++meffRYZGQnuDqlUqtFoSkpKent7XWbJSHB31SeCICqV6syZMzQarb6+/ssvv2xsbByiPQ3Au0QLePm1Wi2Qq//5558jyc0CWutDhw4NToIb+uruD26xWDo6OrzLxb3tpVUqVVtbW29vL5lMrqmp+fLLL6Gm6e4+ysEICgqy2+08Hu8vGn8U/wKoqw0LC3NtZf/rgWGYj49PcnLy5s2bJ06cyOVy/2pqABRFN2/e/PXXX7vf5fH/xJMYxd0FBOzA0fQXWR2jGMUoRjGKUYxiFKMYxShGMYpRjGIUoxjFKEbxXwAXnekoRuECegNQ8eXut/7SObk1AxQlk8kSiSQhIYHJZHK53M7OzoqKCkhO/+visXcLN1WhQvGI10xr/0OBoiibzQZyzZSUlIGBgT/++KOxsREyT7xeByCckEgkU6ZMcTgcR44cMRgM7mSGuNWXEV6Xv6gfGY7jwcHBS5YsyczM5HA4bDZbq9UeOnTo4MGDMpnMo4q9fydc/L9AXuFwOIC4h8vlCoVCLpfb0NAAhbR35XIuziQ3a4WA6iAyMvKpp54KDAyMioricDg4jjudTo1G09jYuHPnzuPHj2s0mpE/VgzDhEJhTk7OY489FhISgiCITqdLSkq6dOnSwYMH+/r6vI5EcrncLVu2bN68GcfxwsLCixcvulkgM4xY0+n0zMzM9PR0BoPR1tbGZDJ7e3uLi4t7enpG3iMVKj1nzpy5adOmkJAQKJ0kCEIoFD7wwAOhoaG7du1qaGgYCRXJX0S0DAVBQUFBAoFAKBQODAxYrVaRSBQdHR0dHe3j4xMeHn7u3LmXXnrJo/wnV0T6Jg1HIpHCwsLGjh3b399fWVk5bF0FVGu/9tprS5cuFQgEMCx6g3maSqX6+PhkZGTI5fLNmzcfPHhwJAFwHMcTExP//ve/Z2ZmAq+k3W6n0Wh+fn7jxo2LjIz88MMPgevVCxKI6dOnP/LIIwwGw2KxnDlzxn0S2qHEmkQiTZ069c033xSLxSaTqbOz02q1QhVdQUHBwYMHoczRu9cdKvLfeuutBQsWcLlcIGyXyWQmk4nL5QYGBk6dOrWjo6O/v9+LGgUgzkpPT5dIJFD3BXTAMGGz2dzV1XVTcYCbgK4MQJWdnZ0dFBREo9Ha29u7urqsVqtOp6utrV27dm1kZCRyg0zQTUBnchKJ1NbWdlM2HJ1Onzdv3sKFC2tra6FYaeisQ+ChXbt2LZPJhE/abDbgOYCaQjKZTKVSxWLx7t27RSLRjh07vJNsCoWSm5v72muvRUREYBhmMBigBMRms0VFRQkEgjlz5jidzrffflsmk7mfTAvw8fH57LPP/Pz8nE5nW1vboUOHDAaDm4PcUazBWgKtqVar9+/ff/nyZR6Pl5OTM3ny5KSkpJycnHPnzuXl5fX09HjRJ4DP57/99tv33XcfjUZTKBQXL148d+6cWq02GAzh4eFpaWlJSUkzZswoKSm5evWqR0Y2hULJzs5+/fXXIyMjoQMLFCUAD7zT6ezr63vhhRcKCgo8epawoEBiP3HixDFjxjAYjJ6eHp1O19fXV1dXBzRA/v7+/f398fHxYrHYIx6PjIyMjRs3Xr169dixYzCUy1IPCQlZsWJFSEhIe3s7ZGAPO8+goCASiWSxWFQq1cGDB3/66afe3l61Wm2z2aBz+yuvvDJt2jQcxx977LG8vDxP7SWwepcsWfLiiy+Gh4dDj4oTJ060tLTU19fzeLzZs2cvXLjQz88vNzf3l19+USgUHu26VCr1119/Ba1ktVrfe+89KI1z8+tDiXVkZOTEiRNNJtM//vGPvLw8eNevX7/+9NNPL168OD09PTExMTg4+IMPPvA0g55CoYwbNy43N5dKpcpksm3btl28eBHKUe12OzxULpcrEAimTp3a2Ng4MDDg5i5GIpGSkpJ27tzp7++PIIjVajWbzUqlEirGfXx86HQ6jUaD8hn3J+waHMpm9Xr98ePH+Xw+lIibzWYMw9RqNWhHlUo1MDBw6tQp9992oVC4a9cuIHkZXJIM0jNlypSgoCCgShu2Bgfeh46Ojubm5pKSkk8++cRlyMGYFouluLh448aNBw8eTEhI8PPzmzx5sqeV+SiKisXilStXhoSEOByOc+fO7d27t6WlBcpyxWJxW1ubxWJhsVgikSghIaGoqMj9vHYURTdt2pSRkQFPrb6+/ujRozA917IMPdRQYg3EP7t37/7tt99c/S5kMtm1a9emTZvG5XJ5PF5oaKivr68X7zqPx6NQKDKZbPv27YcPHzYajTQajclkAk1Zb2+v2WzOzs6Oj4+fPHny2bNngdMMGW4DolAo69ev9/PzQxBEKpXu2bOntLS0t7eXSqX6+vq++OKL8fHxPT09jY2NHtlOoDXhRIiiaGlpqdlsBhZTp9MJlecUCgWsaoPBcPTo0a+++srNNWGz2V9++aW/v399ff3PP/8MTUvgTwRBYBiWlpYmFArb2trcLxEvLi5eunQpGHU3VQbBVOGADmR8QqEQ9jT3V4NMJicnJ8fGxhIEce3atbfeegvkmCAIGo2mVCr7+vqsVitwgwANp/sSkpKS8vrrrwP7mdlsfuutt6AzFnIjJxY+BppusIi7frijWENvDZVK9dNPP7mUP1hpQPdNoVBMJlN3d7f7HPEugDLu6+uDAygsPZBWOhwOg8EAxXypqanp6ekPPvhgTU1Na2vrsOuOoqhAIMjKykIQZGBg4M033/zpp5+AUgjHceh94XA4du7c6RGFAHKjxCsiIgJYNaDCHBx5fD4fuOGYTGZAQIC/v/+FCxcaGxvb29vdGZlOp3/++ecZGRltbW0bNmwoLS29aV8CAmyHw7F37143K9sJgtDr9QaDAfwn4AABSiM+nz979uzly5cnJSUBlYXdbm9sbPSoeBlWY9asWRwORy6XHz16tLOz02KxgDsIHqVSqdRoNGw2u7e3Vy6XuzMsgEKhfPPNN8Cd4HA4Dhw4cPz4cYIgwJ4Ui8XZ2dmdnZ1wEnM4HC5HKpVKdZFM3FGsWSxWbGwsEJqggzrZ4TgeEREhFoudTmdXV9eRI0dcb5JHMJlMWq1Wr9ebzWY6nW61WmFF4HCDoujAwIBIJAoJCbHb7e6zVAGvqUqlOnz4MLg54YsOhyM6OprNZoP94OkJycWtD8wH0PVCLBYzGAw+nw82q91u9/HxAa7u/v5+d/iR6XT6gw8+mJOTo9frN2/eDCQerr/CagsEAjqdLpPJ8vLy3HwVCYJwOBwgxwEBAREREaGhoVOmTElISPD19WWxWMDBMrho1aPTC7AQBgcHW63WxsbG7u5uFovFYDDA0UkmkzkcjkQigacpl8tdTdvcGXn9+vUpKSkwvZMnTz7zzDM2mw3DMH9//+eee27x4sUMBkOj0ZSXl3/xxRdFRUWwzlAX6xrnjmJNpVL9/f1ZLJavry8Q9SIIAseX6dOnQ4uJkydPlpWVeVHDRxAEuCb0ej2CIECFYbFYYChYDpdNDOQ47pjCBEH09vZ+8MEHY8eO/eGHH4AxGvQQlUq95557eDze0aNHbyoKHhbg/SAIAih02Ww2BB2Cg4MVCoVerxeLxVwuV6PRdHV1FRQUuFkRzGKxZs6c+cYbb1Cp1B07dly7do0gCNhhgUIW9gfg7zQYDHq93sWq6s5SwCf9/PzmzJmTm5sbGBjoaoKB3PB/azSakydPekrhThAEmUzWarUtLS3nz5/X6/WxsbFsNlsmk6nVaoFAEBoaOmvWLD8/P61WW1xc7Oo3MuyGwOPxXnnlFTCplUrlm2++abfbKRRKTEzMt99+GxcXR6VSEQRhMpkUCuWNN95YtmyZxWK59Z28o1iD587hcEycOLG8vBzYDlJTU9evXz9+/HgSiVRdXf3bb7/BEcFTbe1wOPR6fV9fX1dXF3hFBAIBhmF0Or29vb29vR0Ia2w2G6hzBoPhprPMbDb/9ttvp0+fhj3RNTGRSDR9+nSbzbZv3z6PVLWr44darQbzAEgISCQSl8tlMpksFgvYaVtbW69cuQLNQocdFkXRSZMmffHFFzweD6YaExMDOhW2b6PROHPmTIi/8ni83t7ekJAQWBAgRx52zWGqFRUV4eHhKSkp0KTCZWzAvZDJ5LVr18pksoKCAvcDEaCVKioqGhsb6+rqzGazn5+fn5+fw+GA7SU4OBgEXSqVFhYWAmXZsMBxfMqUKVwuF0EQh8NRWlqakpIyduzYyZMnz549GwoZgbEWLHg2mz1+/PiLFy/eapvdUayB/JjL5cKBlEQixcbGTpgwgcfjORwOKPcHNgXvyrb1ej2QCQHjRFhYGEEQ7e3tsGERBGG1WltbW3t6empqasxms/t7Ahghg3kIgJJPIBB0d3dXVlZ6NGESiUSj0YAKAwa0Wq1SqfTq1av19fWJiYnTpk2LjIw0Go16vV6hULi525LJ5ISEBB8fHzDQN23aBCddFEWB3Qbc7ZWVlSEhIRwOJyUl5e9///u5c+eampra29ubmprcWRCn06lWq3/++eeysrLXX389KSmJy+VCwTwwnaIompCQ8Oqrr7744ot3oq25LYB6j0qlMplMaKemUqnAViQIYuLEiWKxGEXRxsbGsrIyOJsN777A8fj4eOSGMyc+Pj4iIoLNZrNYLBKJpNPpqqurhUJheHg4CKTNZsvKyjpz5sytaz4UocLevXtXrlzp5+e3YsUK4O+xWCzd3d0ajUYikUDJ8eBInvuAHTYwMLC3tzc6OjoiIiI+Pr65uTkvL6+lpcUVIKVSqTqdTqvVutk1C0AQxGAHJ4qiHA7noYcewjCsqakJ2lq7P8+oqKiwsLCysjIw3VyWuk6nQxBEoVBwuVyJRMJmsw8fPuz+Sx4fHx8cHAwbEdhIGIYBZ25HRweoooKCgubm5o0bN4LvIi0tLTAwsLa2Vi6Xv/fee25ywRAEYTAYysvLly1bBs0SkBve2+Dg4OXLl2dmZsbHx7/22murVq1y82yHoqhEIpkxYwa0ayIIAkiLQB8FBQVFRESAIObn57tUqTvbCxw9odO7SCSCY5Ver79w4cJXX30lEokefPDB8PBwMpkMyuunn366LZHDHcXa4XAcOnSopKQkKysrOzubRqP19PRcvnzZYDBAtzISieR1Wx3gbM/MzDQajdeuXSOTyUqlsrm5ubW1FcQFx/GYmJh58+ZBtzVP4+euWYErKjs7OzEx0eFwHDx40KMMJBKJtHXrVrFY/Oijj97kRQI7qqOj4/Tp008++SSdTne1JHQHra2teXl50MoRzDloD6DT6ex2O5VKBfLciIiIe+65h0KhFBYWHjt2TKFQdHZ2KhQKT3vPwenQ5fNGUbSsrKyyslKhUEBmRGxsrPuk6Gw2e8OGDcnJybClNzQ0gOHE5XI5HA40GAFusDNnzrhPdmW1WvPz8z/++ON169aJRCI4BV65cmXHjh3nzp2z2WxpaWl8Ph/2BLVa/d5771VWVt52e7yjWLvMgO7u7sOHD6MoajQabTYbm82eM2cOgiCuV/+mhQD2qqFvAEIMAoGAw+H4+/vb7fbS0lJgFAfHZGBg4HvvvRccHHz16tXTp08PS2EzBKhU6ubNmykUitFovHjxokd+PRaLlZWVpdVqwd90q2TDscloNLrcC26OrNVqL126dO3aNTjA3HQ+AcZUGo0WHh5ut9t37NjxySef6PV6iJUSnjMj3wS4FgwCISQKheImHymKohBK43A4wNrT1tamUqlMJtPAwMCECROA6Uqn0508ebKzs3MwZeHQDxFO/G+++ebu3bvBt1tfX3/27Nm+vj6n08lkMhcuXAiM43a7vaSkpLCw8E5W01A5IbDWwMjtmhPYmna7HRgy77RkQ4PFYkFcFEVR4AI9evRoT08PeI78/PweffRRCoVy/fr11157rbm5eSSESTweLzg4GEGQpqYmTztcCYVC8OuBi/emXo9AWDx//vywsDCNRuOpUwjaAg7xAYFAAOZfYWGhyWSC/quIh2lbrnxl5Eb8wvV7oVC4YcMGaLcA4VJ3RsYwLD09XSAQIAjS2dl58eJFkGkMw8Ri8dNPPx0UFEQQxKVLl77//ntPEzDBgAQOKlCmyKB0X/DkwC+PHz8+xEnUrb6Mrn9hT4eA35208rC3Aaus1+utVqvBYJDJZCUlJdD5ATJr09PTRSLRiRMnduzYAW/qsJMcAhDuNpvNhw4d8rTXnslkMplM0MtLr9c3NTUhCILjuNlsJpFI0dHRDz30UG5uLoqieXl5HR0dXm8pt4VIJIqKigJPvHcaGkTNx8cHQkhg4QCJempq6muvvZaVlQV0nvn5+W6eOnAc9/HxgYQTnU7n5+dnMpkMBkNOTs769euhe+LVq1f/+c9/unr8eYebdjDXngZdK/74448hBncr33owDAbDwMAAiqKQAuFqvuHRdJVK5c6dO5lMJo/Ho1Kpubm506ZNE4lEoaGhEolEo9H8+uuv33777chlGkGQmJgYCoUC5O2ejiaXy0+dOrVgwYKcnJykpKTLly9Duw8URVNSUmJjYzkcjlarPXr06K5du27bA3ckgLBUf3+/K3MN8URVYxjG4/HefffdiRMn2my20tLS8+fP2+32lJSUGTNmxMTEQFtX4MV866233DzAYBim0+ksFguNRps0aVJQUJBarQ4NDQ0ICICw2oULFzZt2gTJqF7e+S0gCMJms7naxwzrGfNMrMEmAb8pn8+Pj483GAxwCvboidpsttOnT1ut1uTk5KSkpOTkZD8/PzabTRCEQqH49ddfv/rqK/edZUMAXBkWi0WpVEKI2KOv2+329957r6ura8mSJRwOJysra2BgoLe3F8JSRqOxvr7+3Xffraio+CtqYTQaDRhOkP7mhccpLi4uOzvb39+fRCLFxMRA0zPwMyA3zpH5+fmPPvqomy1YIR28pqZGq9XS6XQ/Pz+RSARbt8PhaGtr++CDD/Ly8gb3IbhbIAgiLCwMjIWzZ8/CO3+nq3isrcEfDNkX4HYFD6KnUzSZTKdPn7569WpgYGBKSso999zD5XLz8/MPHTrU1NQ08hoFAIqi4Obs6+uDiKan86ypqXnjjTc+/fTTgIAAMHAJgoAwmEqlgqZkd/0RAqxWa3FxMcR6XO0bUU/KlNrb24uKimbMmMHlcqF9iuu+bDZbb2/ve++99+OPP4L3yR3AF8+fP//jjz8uWLAgICAAx3GtVltdXf3HH3/8/vvv0JXGi5sdFjabbf/+/RKJpK2t7fr163e5bIpEIk2bNu348eP79+9fvHhxaGgol8sF56vXY4K1PbgX/N0CiUTavXu3Uqncu3cvn8/3enz0Ftzded72itB5KDAwkMViQZMQULTuuxHJZHJgYOC2bduuXLnS0dEB58Lu7u6ffvpp9uzZ0B/Vu7nR6fSoqKhp06ZlZ2dDWP7fsCZMJnPGjBlTp06FWM8Qn/RGW3d3dzc1NdXV1cnlckhtcW1D3k33to7CuwXoGAt5pF4P8hfNbegrQrckBEFAM4Ff2aPqKWgj9sorr7zyyit3d24mk6mpqQnO0P82GI3GCxcuEDcwxCc9FmuCIJqamrZs2QKekH//8/YUAwMDSqUScrO8ME//g4CIveu/nrpx/vfhpvjx/2n8RebNKEYxilGMYhSjGMUoRjGKUfzvx//mgxSGYRwOByp/IWHrPz2jUfyb8L9QrDEMo1KpIpEoIyNj4sSJ06dPVyqVv/76K4TT/gc5+EZxJ7jSJ6EKzoPqmL8UkN0aHBwMXb6rqqrOnTvX19d3V7ySBEGQyWSBQAC8UCKRSCwW5+TklJaWeldQPCzQG/R24Bf3NPfLNQiO4ywWi8fjicViFotVX18vk8n+R9DG/nsAvlqxWDxr1qysrCwajcbhcD766KPr16/fRDl5s1gPG7CANH8okIY6H08nx2Qy4+LiDhw4EBAQAEFXp9NpMBj6+/v7+vqeeeaZsrKyET5IgiA0Gs3Zs2ctFsvYsWPhpubOnSuXy4EyaiSDI4NEUCKRxMXF+fn5RUVF+fr6EgRRXV196NChlpYWj9JaoO4rMDDw3nvvXbZsWWhoKEEQLS0tn3/++bFjx+5W5hCGYUwmMyEhYebMmaWlpbW1tb29vR4lV0BeimvO8MNfGiR2XQs4LaZPn/7MM8+Eh4dDMeWVK1fYbDYQC/7L528dgkqluggjb5orvC4sFmvy5MksFuv06dNqtdrT+yGTyWKxeNeuXZmZmWQyWafTAVELh8OBAoWFCxeeO3fOwxv/l0kC/RKZTGaxWBwOh8Ph+Pj4JCQkVFZWHjlyxDtSSdfgUA2emZm5YsUKPp8PNaQMBoNKpeI4brVay8vLX331VWB+cnNMKpU6f/785557LjExkUajITeSimQy2T//+c8DBw7I5fIRyg0QAG3evHnChAmQgN7e3r5r164TJ064uYNBpmtwcDBkhwYEBGi1WqlUKpVKXVmcLhG/i1IOVmVsbOyyZctyc3PDwsJcdV/Hjh376aefSktLb9LW/0+sQaVBRt6tZUiuz+A4HhUV9c477+A4/sEHH1y6dMlTywHeDSjRpdPpSqXSarX6+/tv2bJl3rx5TCbz+vXr06ZN8/qEB282jUYjkUiQrEKj0cDU9vX13bNnj6c8IYOnLRKJ7rnnntzc3OjoaAaDYTQaTSaT0Wg0GAw0Gi06OprP59tstq+//vrNN990JwMbciE//fRTuHdQh8AjAzdisVjq6+u/+OKLn3/+2WsLCkVRPz+/lStXRkZGlpeX19TUCASCxYsX2+32N954o7u7e9ivQ+FSQkLCsmXLfH19+Xw+lBiXlJS0trY2NjYiN8pY9Hq9VCq1WCxqtRqIgbwWcRDo4ODg9evX33vvvVwuF2rkbDabWq1ub2/fs2dPYWEh8KAP/uL/095Aw4UMt5uQSKT58+cnJCSYzebAwECPuG4BBEFAfWtDQwP8BkVRuVz+1FNPKRSK1atXMxgMkUgECfteAMY3Go0QMycIQq/XQwFpTExMdHS0XC73NL8C8ulSU1O3bduWnJxMIpGAUuLYsWMymay9vR0S2x966KGnnnqKTCbHxcVRKJRhU2FRFOXz+UePHk1LS4McG61WW1JSUlJSMjAwkJWVlZ6ezuVyk5KSPvjgAzabvWPHDu/SPnEcHzNmTFhY2JEjR4AShEwmh4SEuPL4hpU8UHNms7m3tzc1NTUwMJBEIikUCtCjEonE398fKBQRBIF/VSrV7t27jx496kUpN9AM+fr6LliwYPXq1REREWQy2Ww2uyhNEAS5du3a5cuXgTzj5vt1/eR0OkH9DFEwh6Io8AwxmUwozxxJcu3gSzidTpPJdO3atYkTJ6IoCoymXr/lt57brFZrXV2dv79/UFCQr69vd3e3R4OjKMrj8WbMmJGQkEClUmtra99///3CwkK1Wg3LBcYJsH4B49Gwpg4o4xUrViQkJMABo7u7e/Pmzfn5+UDBunfv3oULF27evDk0NJTP57/88st9fX1HjhzxYs2pVGpmZqbT6SwrK3PVOzudThqN5s6WAmrYYrHI5fLm5uba2trS0lKbzdbZ2dnZ2QmZyRwORygUCoVCFoslEAhcXJWVlZX19fUerTaGYUFBQUuXLp09e3ZQUBDQpyiVyurq6iNHjly8eBF42Mxms0qlslgsQ4m1w+EIDg5ubm4eqkQMxyMjIw0Gg1ar7ezsrK+vH3knd9dpIDo6eunSpeHh4c3NzW5WQQ+NwTdCEIROp6usrHzyySeBkdUjglASiQRPS6/XFxYWvvDCCx0dHa62AbBHk8nkGTNmgGUslUrd2RCAPh1qEc6ePbtp0yagPIa/mkymPXv2nD9//sCBA4mJiSKR6OOPP+7r67t+/bqnpL2RkZHZ2dlvv/02nD7h+MFms/v7+908acAeqNPpSkpKgMkJQRAg24Y9RyqVhoWFsdnsiIgIIFehUqkGgwEoUNy3tslkcnBw8O7du2NjY4GpzGg0dnd3nzx58uTJk319fSaTiUaj0Wg0V1XHrYP8P7GGil+Y5a0nRVgLOp0OBpNKpSovL/eISmYIMJnMzMzMJ598Mj093WKx9PT0eG2BDAGHw2E2mx2O/6+9946L6kzbx0+Z3gu9DL1XBUQREFGxa2yxxFg2bdNN8mbTE2MS04xrktUkmkSTaDR2MUYhFlBEioBIG3pvMwwwjelzfn/cP+fLosIU8ia7L9cf+2ENPOc559znee7nLtdlAtormwDdbhqNprS0dNeuXe3t7cP3NDiTxMTErFq1ikQiDQ4OnjhxYsw1Ff72xo0bcNfvvPPOcJu2zLmlpeW55547c+aMUCj08PDYtm3bypUrQWrIysmjKJqRkUEikQYGBuB0RKfTZ82alZKSAiIK1j8EtVoNZA+WaCaCIKCOotVqKyoqgAQ9MDBw/fr1UVFRbW1tcrncSpZh8PTi4+M///zzkJAQiFtUVFQ0NDRkZWXV1taCyIaFKa6/vx/H8Xse7f6fWcNJBblX9AMAj0MgEAgEArPZ3NbWhlgRELTmYZHJ5M2bN8fFxcFbPHny5ODgoCNj3g9A4wmnMZtmSBCEXq+XyWSwYgGZhMUEMQzjcrmffPIJl8s1GAyFhYVWUqLp9frBwcFbt25VVFTcj7mKIIjW1lZwS6CHDXjjrZ8/hUJZtGgRn88PCwsDJpa5c+cGBgb6+vrW1dXZdOInCAIWPuTfqRqAu0OlUgF5YmdnJ5wTqFSqp6dnf3+/NQEAEom0dOnS999/38vLy2Qy1dfXHz58uL6+fmBgoLW1lcFgBAcHq1QqhUIREBAQHx8PzKb3Hmr4/7l7gYH9l81m8/l8DodDJpPd3Nzc3d0tNJXDv1r7gKJocHDw1KlTORyOUqns6ekpLCz8I3IQFAoFOP1hA7Vp2vCbcrmcyWTC9tre3g7OA4IgLBZr8+bN8fHxBEG0t7dv2bLFSjJF4Mi7cePG6GTYEKaEn7VaraUl0UpwOBx/f38Wi/Xqq6/evHmTIAiJRDIwMKBUKm1t1hoeooY9Cv4dFkR4Gnw+/5FHHpk2bZrBYPD39/fy8hKLxZaA9/02MQzDPD09n3jiCSAM6+/v/+KLL65fvw7/FZi5QaCCzWZDxzRBEGKx+J5R1DGyjHBUWrx4cWhoaF1dnUKhgOxOf39/aWkpZBwctD8URVNTU6EbksViTZ48ec6cOQcPHrSbCe2ewHE8MjIyLi7ObDbX1tZaSE6svAQEAXp7e318fEAj0Gw2X758uaKigkajzZs379lnnwXCjS1bttiU8RkaGmptbQVJAIu6DXGHlQXiratXr4bYgslkOnbsmK3yQkajEVjljUZjY2PjtWvX6urq3N3dg4ODQVDByqneDYulQpMllUplsVhz58594IEH+Hy+QqGora3t7OzU6XTQEzjKJ4RhWHBwcFBQELya3t7e7u5u4JKl0WgsFotEIoFOQ3BwMFDK+Pn5OTk53TNzMppZYxjGYDBcXV2FQiEsTnw+PyYmhslkNjU11dbWgoSC3Q8FgOM4iUTq7u5mMBg8Ho/P569Zs6ampubGjRuOhGmH/8xgMOLi4hYuXMjn8y9fvgyhe9R25g0gfQwODsYwzM3Nbc6cOQsWLAgMDIyJiXF3dzebzUVFRVeuXLHpPKfT6RgMhq+vr0ajEYlEra2tENSHkxyO41OnTn322WchmVBYWPjNN9/AVmb9tNVq9bZt2zQaTUlJiVQqhUCyVqt1d3cHKm7rZzsCsF0jdzxJLy+vlJSUNWvW0Gg0pVJZXl7+3XffNTQ0ANvE6HPGMGz69OkgF6FWq6uqqiA+DUwH8PkBbbSLi4vRaGQymYGBgffTAPo3s0aHqQ4gCAKOub+/v0wmg0ROUlISMK9BRmNcWudRFL127Vpzc3NbW1tAQMBTTz3l6ur64IMP1tfX2yRJg97hs0IQxNXVFewM9H6mTZtGJpPb29vPnj1bWFgI79IyeWu8EThaQOgADuNBQUGJiYnLli1zcXEBr6Crq+vll1+2nkkRQRCCIIBhefny5e7u7vX19ZWVlampqR4eHhQKpaenZ2BgICkpic1mm0ymhoaGf/zjH7A42bSPGY3GkydPjpAadHd3DwkJaWtrc+QlgguKYRibzU5NTV2wYEFsbCwcvSoqKvbs2VNfXw+MpmPujSaTqbe3FyhopFLp1atXxWIxsGziOK5QKDo7O1UqFWxfvb29kD24X4XCv5n1iN+AZCnwgra3t8Op02AwGAyGq1evjguJEcTFpFIpqCUUFBQUFha+++67kZGR06dPP3PmjJULNoqiHA5n1apVZrOZzWYHBgbCD7GxsSDsUlJSUlZW1tbWptVqqVQqQRBGoxHuaMz3it4Ru+BwOM3NzQqFAqIHvr6+TCaTSqWazWaZTLZly5b7EXiOAjab/dBDD02ZMgWyoWazOTw8HHijRSKR0WgUCAQEQXR3d7/22mvV1dV27GBwSh7xj0AAmZmZ6UgKEAgpORxOXFxccnJySkqKQCAAzobz58+Xl5db6DDHHM1sNl+5cuVvf/ubp6fn7du3KyoqlEolNNuDXBHssRQKhcPhiEQis9nc2Nh4v1jcvZ0Q2FwgZCiRSFpbW0ESKj4+XqVSHTx4sLCwcFwi1kwmMzQ0FNwvyIs2NDSUlZU9/fTTs2bNyszMtHIoKpW6dOnSjRs34jje1NTU0tIColt0Ol0sFmdmZkKJSGxsrK+vb1dXFxzMjUYj0HWPHniByGZ4eDiDwdBoNGQyGcOwwMDA9PR0BoMBWcwPPvggOzvbjgpEJpMZHh4Oji/o6125cqW/vz8wMDAtLY3H48GaVFtbW1hYCEuJHe7T3XeUmJgol8vPnj1r9wgQYI6MjJw0aZKbm1twcDCLxYIAyI0bNwoLCwcGBmwyku7u7oqKCqinMJvNLBYLlh7QZoCdzcnJ6W9/+1toaKjZbG5qarrf2vr/zBpELYb/N51OZ3E2cBx3dXUFKzl+/Pg9ubJtBYVCiY2N9fDwaGxsHB4sS0tL43K5YWFh1h/So6KiFi5cyGKx+vr6KisrcRxXqVRQ7AoivMBeGRQUFBsbm5GR4efnB8oVFy9ePH36tFKpvOcLgAkAmaKTkxOO4yKRyMnJyc/PD2jWQPImPz8/MzPTjiIW2MRh7QdfCCjigQeMzWaDe2MymZqamjQaDTwlS/bHJodnOMhkcmJiYk9PD1BG2QGIaUZERGRkZICzCyIeCoXi+vXrx44dq6qqGv6RW5PIVKvVV65c8fPzc3V1nTZtGovFkslkcrkczBIscOPGjQ888ACCIF1dXWfOnLlfAf2/pWNGXAbOFvAQcRyPiIhwcXGRyWRjCrlaAwzDvLy8UlNTJRKJJcyEYdjChQvj4uKg7NDKLwdFUV9fX1DGhlKQmJgYiURy4sSJgYEBoGYFbbXW1ta2trbVq1dHRES4u7vz+XwEQY4cOTLK7UBCzsXFJTo6mkwmy2QyJycnf39/f39/4B4pLS3dvn27rYKrFgD7vYX/DcQd4dQI9ZZGo1Eulzc3N1tK5CypbCsvcXfYZPbs2Z6env/4xz8c8UCoVCqHw2EymVCVAfUC2dnZe/fuBcVbWwc3mUy5ubnQ/AGqhY2NjQUFBRQKRa/X8/n8zZs3L1u2jMVi9ff3f/DBB7dv377fbvBv6Rjk389Pw4OUEK/g8Xg1NTWOux8IgpBIpHXr1q1fv16lUimVyuLiYhqNtmDBgldffZXH4+n1+h9//NF6xxrUlYaGhnp6eoAwPC8vr6WlZUTQQKfT3bx5UywWnzt3bsaMGUFBQY2NjaPX1oK2S3x8fFRUlIuLCzCFcrlcqKGtqKh47733ysrK7NPQQRBEqVTeuHGDx+MJhUJQeQQqf+QO/Q0IHx47dmy4OqYjcVUmk/nqq6+KxeIzZ87YNwJQCbNYrJiYGHD9TSZTd3d3S0vLvn377LNpBEEIgujr68vJyUlNTXV2dnZzc0tLS9uwYYNEIkEQBEVRUEaura3dvn37hQsXRsmPjvStR5kNLIc3b950pF7ZAldX19WrV4tEIhRFd+/ebTKZqFQqlIIolcpPP/307NmzVj4as9lcUlLS1tYGZZxQ6Xq/Fw/rSk5OTl5eHgiIjZI6we7A09PT29sbVlMEQfR6PYho7dmzp7Cw0G66VIIgZDLZ6dOnnZ2do6KiIOEFxdDASF1UVHTp0qW8vDwI2Q5faKzHcF+OSqU+8cQTUF5iK9fmiFWfxWKBb2YymSorK2/cuHHt2jVYSmwa1gIIOxYXF9fU1DCZTAaDAfpEbm5usGVJJJLs7OyDBw82NDSM3qVhVdMXJEoYDEZeXh6UNzmeM+/t7f3ggw+2bt0KSlZQGw1FYS+//PL58+dt2hM0Gg0k862E2WwG6eLRfw3uEbhuoXQdXOG6urozZ878+uuvYz7fMWEwGG7evCmVSqdMmRIXF+fp6alSqQYGBm7cuNHY2Njb2wuirHfvpdYDDltsNnvx4sWbN2/28fFpamoCaVqbxrGYNYDJZLLZbBqNplKpQAulp6fnnjZtffLIZDK1t7e//PLL06ZNi42N9fHxYbPZFApFoVCcP3/+3LlzQPs4PqSs0EC2cOHChQsX+vj40Gg0O8qs7wkcxwUCwezZs994442FCxfyeLzxGnm8QCaTPTw8NmzYcP78+fr6+urq6p9++gm0mu45VZty0RaAq+rm5ubp6enk5ESj0Uh3YBnQUolxd4/T6EBRlEqlzpw588aNG319fXV1dSkpKQ4+ZwqFkpGRcerUqatXrz755JP3e3Hon8QUN/b14NAtFAoh0gRR2z+Iw/ivCfBDRCIRhUJRKpWWRN24X8jxPXCUkVksVmJiIofDOX/+vONuJJ1Onz59+urVq/v6+n766SdbS6b+aFj7GVkiFeNyXpzAfzpwHBcKhRBzhHLfP3tGE5jABCYwgQlMYAITmMAEJjCBCUzgHrC03/3pgGmQyeT7zYdCoXC53JiYGCqV+heZ838K/psflqVIi0aj8Xg8Fovl4+ODoqhSqUxMTLx582ZRUREUDP2JYfh7xqopFMrUqVPfeOON8PDw7u7up59+uqKi4o9QNB1fWLrUkDvqZH/WTP4cxtT/NQC1n7u7O41GEwqFTCaTIIihoaFz585ZpOGtKe+EFwZ/gqIoFCSBKJ5MJtNqtcCfbav0mVAovLsQnkwmr1y58uOPP+bxeDqdDrTKbbUSi6ogVD34+Pi4ubnFxsZC7Y1er5fL5cAuCfk1x00Qx/H4+PiPPvpIIBBcv3799ddf/yO0dK3E2C26UK5FpVIRBIFeEpPJNO6d4TiO83i8iIiI0NBQqVRaX1+v0+mg2tPuaD+0tLi6upJIJLPZLJFIdDodm812cXFBEKSpqUmn0+E4DvwEo98OmUzmcDhRUVERERFeXl7h4eEwOLQYDg0NVVRUnDhxory8XKlUWr/23y12TyKRnnvuuddff51Op/f19UEpoh3dynQ6ncfj+fv7v/7661FRUcBIiCAI/C8kunU6XUlJyYcfflhcXGzTtO8GiqJcLnfr1q0JCQlarba/v39cKvLtxn3NGgza2dl5yZIls2fPBoYQs9k8MDDQ1NRUXFyclZXlIFmZBVAZsnbt2pSUlPDw8La2ttOnTwMdFqyIdvCykkgkNze3xMREHo/X1tbW0tKiUqkGBwc5HI6vr69IJAJpZ7PZTCaTSSTS6EWwJpOJRCIxGIze3t6goCAohoZOGZPJ5O/vHxwcPHPmzE2bNt26dcv6SY54eiiKurq6btq0iclkDg4OvvDCC/n5+UKhkEKhABerlcOC98Xn859//vmkpCQajYbeITAa/msUCiUpKemjjz566qmnSktLHXmVGIalpKSEhYWZzWYoDx4vvw5qYIBq+W9/+5uLi8utW7e2bt06OmXFaKs1jUZLSkr6n//5H3d3d/QOITnU2Tz88MNXr1594403amtrHUycgp/g4eEREhISHx+PYdjg4CC0dkIptq2lzFD4P2nSJOiCuXLlSkNDQ29vr8FgADZElUrF5XIt65PZbObz+VDUez9At2JpaSmUzorFYuB28fHxAYr1oKAgJyenxYsX22TWI8Dn87/55puAgACTyXT69Gmg6NVqtbbWNoGjBfyRCILA7gp9qDiOoygKRIGgNi0Sifz9/YE90O6ZC4XCBx98kEqlqlSqsrKywsJCx5dqEonk5OTk5eXF4XBcXFz4fD6JRBKJRK6urh988MEYfzvKf2Oz2WvXrgVuTPA9LDVlFApl3rx5QHTS3Nzs4KcJhTjBwcFkMlmlUmVnZ1dXVwNro302nZqaOnfuXAzD9u/fX1paCqUL0L1mMpkGBgaMRqNarQZXCu5u9GGhV6inpwfDsM7OToIggDwbGhCh2pMgCEfEkslk8qZNm5KSkhAEuX79+quvvgpOv0ajsaMUx2g0ymSyc+fOATd+bW1tQ0ODXC5XqVQGg4HP56enp0+aNAnoUuHIYffMURSNioqKjo42mUytra0HDhyor693cEAymbx06dLQ0NDCwkKxWFxUVASUQxKJpLa2VqlUjj7CaE4IEGQZDIahoaHu7u7m5mYgZ3B2dqZSqRQKJSIiIjg42MGmfARBgEeLyWRqNJrr16/n5uYOr5q3HmDTaWlpTzzxRENDw9dff93U1GRhNAWKFgRBTCYTdMiZzWZYxqwMn0EbCAyo1+vVajWKogqF4siRIw8++CCDwSgvL7fvdaIoGh4e/tJLL7FYLIVC8d5774G7DysriUSCb8/6wQmCUCqVOTk5BoOBwWD09PR0dHTodDqhUDh9+nQgh4eKc2BxcPANxsbGMhgMtVqdmZmZl5d3Tz0XKwFltGlpaVOnTt2/f39tbS2sPkNDQy0tLXw+/+TJk2MOfl+zhobqDz/8cGBg4ObNm9nZ2QaDISIiYtWqVatXr0YQxGw2q1QqC8mi3cAwTCAQ+Pr6qtVqJyen33//vbW11e4zYkpKyurVqwcGBr799tuGhgZLTyv0bpHJZFieDQYD7Lkoitr3AiyNKvDZM5lMHMdtIjYZDhqN9umnnzo7OyMIUlNTU1dXZxkfvGQKhdLZ2WmTn6DT6RobG5VKpb+/P4/Hi4yMXLVqFazQFubz0tLSrKyspqYmuJDd3ySQWxcXF9+6dUutVtvdAofcuWVXV9eurq7a2lrLmQfH8RdffNHT01MqlY45yGhmDc08W7duRRBEr9d7e3uD+ws8G3q9/ty5cxbTsRs4jkdHR7u5uQmFwqGhoezsbPtsGlpcFy9ezGQyDx061NjYaHmy0Abh6upKJpOhJQzcEqPRCOu3g7cAkiMSicS+Rm4URdPS0qZNm4bjuFqt/u677wwGA4VCgem5uLjExcUFBARcvnx5lKbUuwEel1wuZzAYa9asSU5Odnd3h0gIQRA6nU6pVDKZTGDoq66uhk5hO8wRw7BJkyaZTKbBwUE4QzvoWMM9jtBImD9//urVq7Oysqz5tkfzrWEp0mg006ZNmzVr1syZM0UiEZyZ1Gr1xYsX33vvPcfFDl1dXQUCAWzuW7duHRgYsG8cFEUDAwMDAwMHBgbq6+vBUiHSPHny5PXr10dERHR0dOTl5bW2thoMhvr6euggcvAdoCj69NNPYxj266+/2vdBMpnMN954g06nm83mrKyswsJCEonk5+c3NDQUGRn55JNP+vv78/n8hx566KGHHqqtrbX+IwStqfLy8p6enhEskiQSic/nx8bGxsTELF++/JtvvikqKmpsbLTj4MhisVxdXbVabWdnJ4ThHeyHgIOBu7s7yBjBbLds2UIQxGuvvWbNCGMcsWHL/tvf/jZ37lyIE0HZuFgs/vrrr+2Iu40AbDcrV64UCoUYhpWWljrS4u/i4uLk5DQwMMBkMmk0GkEQnp6eGzduXLZsGWj4NTU1RUVFiUSiuro6Hx+fvLy8rq4uvV7vyGsAVj6z2fztt9/aMQiKoklJSZGRkQiCKBSKvXv3GgyGJUuWTJkyhSAISKM4OTmxWCwWi3XmzJmlS5daT+4Pwave3l4YNi0tLTAwkE6nA/MEjuPQFMzlcrds2XLkyJGDBw/a4UeFhoby+fy+vj4GgwHZHzvO+sNhNpsvXbo0efJkT0/Pjo4Og8EgEAgCAgLUarWVh/KxzVqv16tUKti8kDvc2gEBAQsXLrSQpto3e+ROD72bm5uLi0tHR4fdbCwwFISiGQwGNLpGRkZu2rQpLCxMqVRev3796NGjlZWVnp6efn5+Li4uEOG5ePEiMLvZ7Yf4+vqSSCSFQtHV1WXHn+M4vnLlSjqdDoEUf3//5cuXz5gxA/r8JRIJaLRFRUX5+vp6e3ufOHFi1qxZ3d3d1l/CbDbX1dW98847np6esbGxUqlUrVbrdLpJkyZt3rw5KioKKJKTk5NpNNrOnTtHqGaNDhRFp06dSiaTnZ2dY2Nj29raFApFVVWVg1x2QIQZGhrK5XLlcrmzszOO4zU1NVa+prHNWqVSffbZZyQSKSkpydnZGQJ8bDZ73bp1DQ0Ne/futVVeaASAigr4jxkMht2WbTabW1tbb9265enpyeFwgoODZ8yY4evrW15e/sEHH1RXV0O8rKOjo7W1NTk5OTg4ODIysry8vLW11ZoXcM8VHUXR5557DkVRmUxmX4MglUqNiooCPxhmEhgYyOPx+vv7S0pKDhw4UF5ejiCIh4fHyy+/vGLFCn9//02bNn300Uc2GY3ZbNbpdM3Nze3t7ZZDmFgszsrKio6OXrFixaRJk0JCQtzd3Q8ePNjc3Gz9yCiKxsXFwWfp6+sbHR3d1dVVUVFh00O4J7RabXl5OaSWIDnw5ptvWvm3Y8f5jUZjZWXlCy+88MADD8yaNYvP55vN5oSEBDab/dJLL128eLG2ttaR71KlUonFYg8PD5VKBeVsdnNuSCSSqqoqZ2fnxMTE/Px8CoVy9uzZL774ApLwFjoEDMMiIiI4HI5UKrUy6A57FIlEAtp92KNQFJ05c+aqVasIgrh+/bp9xT2QIYIzoo+PD8ivNDc3X7x48cCBA52dnWCFGo3mo48+io+PDwwMjI6OHj0tCqYw4r5gbsMnCdykV65cKSkpWb9+/datW93d3SdNmmSTWZNIJKFQCLkemUzW0NCgUCiGN8w7AstbmzdvHnzn1s7Kml8ym81yubyioqKmpqa+vp7JZL722murV6/m8XhLliz55z//6YjiMkEQ3d3dsGCDnpDdMBgMXV1dcrncxcUlLCysvb392LFjvb298HTgd3Acj4mJiY6OHhwczMvLs6YcB2LewcHBjz/+eGRkJJ/Pl8vlJpOJwWBERUUBg1l2drZ9MTKTyXT27NkpU6aAj06hUDQaTVNTU25uLtg0DKjVatva2goKCnx8fIRC4ShGA3FfgUAgl8uhMMMyJeIu9QhIURkMhqioKJDU6enpsWn+Tk5OkZGRwE11/fr13t5erVZLp9Nt5dYZBSiKPvDAAx0dHdZzDlpLFsFgMOh0emtrq0wmA9kliOZkZGTYqvkwArCukMlkx6n9gD2sqampt7cXJFZBkAW9AwqFEhQU9OijjwoEgosXL+bn51spqIDj+Lx58xYsWBAXFxcaGpqUlJSSkhIfHw8H09u3bwPtPCznNi1UWq02Jyenvb3dbDYzmUzIxstkMqlUColu+DWoJWIymZYq7VGm6u/v//7777/11lvBwcE0Gg2KXkgkEoVCAbpoyExBLJ/H47366qsPPfQQ7AAikcj6ySMIEhAQAOSle/fuzc7ONpvNc+fOjYiIGEe+FxaLJRKJbDrLWrVaQ/nvokWLjh8/3t3dbTabgXsYwzBLKNQRUCgUg8Ew/GBqHwiCUCgUkOoD/U94f8D4ymKx0tLSQFTywIEDx44dsz4ZBhwparWazWYPDQ1RKBQajQZVjQqFAso7oebT1npDk8nU3Nz82GOP/fDDD6DMC2SkEBvp7OxUq9UQsliwYMGUKVMMBgNwgd9vQC6X++mnn06fPt1kMvF4vF9++UWr1XI4HC6XC4bLZDK5XC6o0/r4+MTFxcGBDJz7K1euWD95FEXpdHpHR0dlZWV7ezuHw1m8eHF4eHhNTc04lu9NnjzZaDQeO3bM+j8Z26xhnVi1alVqaiqE9nQ6XVJSEujtAROpA3NGcByPjY2FM5OVSkL3A1hzS0tLSEiIQCAIDg6WSCQMBoNGo3l6eq5cuXL69On9/f2ff/75uXPnrN/RIHlx8eJFDMOmTJkyNDQ0NDSUkZHB5/NRFBWLxTU1NUBlBqLOtk7bYDCUl5evXLly48aNGRkZKpWKx+MtXLhw/vz5UFMVEBBAIpGSk5OdnJykUunhw4dHuYqzs3N8fDwUe6xevXrRokUEQYCDB7VNlh3AsmbDPfb397/zzjvW5PAsQFGUx+NJpVI6nR4ZGZmSkpKamiqXy/Py8saROQTIv3Nycqz/E6vM2s3NLT4+ns/nR0VFTZ48WaVSzZ49m0ajmUym0tJSBzMyBEEUFhbOnTsXAm0ORvJNJpNUKm1sbJw5c2ZISIibm5tarYYf3N3dc3NzDxw4YEdy3mQy1dTUNDY2AgO8p6dnbW1tZGSkh4dHbm5ueXk51LiOIkA8CiChW1dX99Zbb3388ccgJx4aGhoeHp6SkuLi4sLj8Wg0GtTM3Lx5E06999tn+vv7odAFthRwjeA/DSfRsxg3ZFslEsnDDz9848YNW/1AqBP09/d/7bXXIK32z3/+0yZRqDExffp0lUplU9hxbLMmCAKUDUBG8o033qDRaF5eXnq9vqen58CBAw4G+IxGY15e3syZM6FU0pGhkDsLdnl5uclkio6OBi1nEonU0NDwww8/FBYWWqSRbQXEyFpaWkB3sLe3t7GxkUQiDQ0NDQ4OWjjVweDsuAQYt1wul8vlra2teXl5XC7XxcWFwWDgOD5nzhwXF5fW1tbr169b6rfuif7+/u+++2727NksFgteHORcRlxLo9EMDg6q1erm5ubDhw/DYcmOs01HRweFQnF3dwdFud9+++348eOOhBDuhqen57Vr12yam1VmXV9ff+XKlQULFri4uLi4uMALbmhoeO+99+z4vkfAbDb39PTo9Xocx8FbdRAQt8rNzb158yaLxTKZTJBUc7y7zhI3UCqVtbW1AoGASqVSqVQajWbRisdx3Joz6JgXguySpZSgpKTEokU7+gM3Go3vv//+4cOHIRUgEonA0zCZTHA8AKlwKMjW6/VGo9FuDlKz2VxdXb1z5845c+aEhobm5eXt3bvXJoXfMQEbuMlkApFzK//KqiOjUql88803+/v7H3roITKZ3Nvbe/369UOHDhUWFjq4VAPodDq0djroW1sAK59CoXAkbXk/QATNxcWFSqV6eHjU19cPDQ2B9g+8gHF8qRYQdzSOrYFer6+pqYGfq6urx30ywzE0NARq5H/Q+BDOhyPB+FNvondkgWJjY6HgaRwJXqEEjMPh/KfQBsD6By2eEBH6s2f0X4uAgIDu7u433niDxWJNPOcJ/PfgP2Wxm8AEJjCBCUxgAhOYwAQmMIEJTOC/Cfc8j08c0v+a+Eu8FeAMCAsLS0xMHBgYAAHc8U3AOggURRkMhl6vh1mRSCQ6nR4REbFmzRq1Wv3TTz91dHRoNJoJZaC/NGxahCDrBg28o//m3eF0DMOCgoKOHDkCsvL9/f19fX3d3d0HDx4MDQ21laTrfheFsno+nw9ZJMfHpFKpK1asuHnzZmtra1lZ2XPPPefh4TEKU7WtgMYFi1Iji8VyvPr3/xTubTdW9vZB8VNiYqJQKKyoqMjLyxudJ/NuJkVPT8/jx48HBQWhKCqXywsKChQKRXh4eHJy8o4dO7Zt21ZcXGx3vhRInmJiYlasWBEeHt7e3l5SUpKXlwdcqfaNCcOy2eyFCxdyOByz2dzf328wGFxcXIADze5hYWToJEhPT1+1apW/vz9Uocjl8pKSkm3btrW1tf3VNgQcx5lMptlsptFoAoEAujCbm5sdmSckcdlstlAodHd3F4lE7u7uarW6oqJCLBYDI9foI9i5HOI47uLiEhUVtX379oCAALlc/ssvv8hkslu3bll/PzQabceOHYGBgVBNBT2/KIqmpqbu2LFj0qRJSUlJpaWl9tkKlAK/8MIL69atg5oko9G4YMGCa9eu7dq1q7S01JHnTqVSgWyyqqrqq6++GhgY4HK5Tk5O3d3ddteE4DgeEhLy9ttvT58+nc1mIwii0Wj6+/t1Oh2dTheJRLGxsR0dHfZNG9Z+NpstEAj8/PwmTZq0bt06oVCoVqurq6vffvvtiooKO54zn89/5ZVXfH19/f39BQIBl8uFNoXdu3e//fbbjnzkUCKfkpISExOTkpLCZrM1Gk1BQcHPP/987dq1P8SsQS85LS1t7ty5IpGITqdrtdqmpiaZTGb9G6VQKC+88MKcOXOgZeiRRx6xkK8WFxffvn177ty5Hh4eo/sM9+sGp1KpU6ZM2b59e2xsrKXYFSi0U1JSzGbzli1bZDKZ7beOIAiCYZhQKGSxWBqNBmTPTSaTk5NTYmJiTk4O8L/YatkYhkVHR3/11VceHh5DQ0OVlZU//vjj1atX5XI5k8l84oknoB7djjo7DMO8vLy2b98+a9YsBoMBjH7QBgZrk5+fX3x8fEhIiB1lYQKBID4+3t/fv6ur6/z588HBwdCFvmbNmj179oygZbIeUDdrMBjodHpISAhUh/f391dXVwN10Zgj2GzWwDKTkpKSkpISGxsLrPeDg4Otra0SicTK546iaGRk5GOPPYbjuEql+uKLL4aTFUG3yMyZM/l8/uhmfbf1YBjm7e29c+fOpKQkJycnKM4ENhaovudwOMnJydOnTz937px9Kx+GYWFhYcHBwTKZDLQvKBSKq6trcnJyX19fQUGBHR4OnU5//vnnnZ2dOzo6Pvzww9zcXEt5J3R0EwRhB1U+iqLOzs6HDh2aNm0a9IzqdLqBgQGNRqPRaDw9PeEJ8/l8oVBoh1nL5fKbN28WFxcfPXq0s7PTz89v586dsbGxRqORw+HYOpoF4Hr19PRUVlaGhoYqlcqBgYHs7Ozz588rFApHycruBoVC8fLyioiI8PPzi4iIgF5lmUz266+/Njc3Wx+7wHHcstVmZ2dnZmZanHIURQ0GA0RCrOluHL5gg9U++eSTaWlpbDYbRVGNRqNQKFpbWzs7O4E8hMfjOTs7P/PMMzdv3gSiBZueAHKnS43NZlvK+Xk8XnJysr+/f3R09O3bt22lBALjCwgI6O3t3bp165UrV8CCoRQzPDw8LS1NIpFYT/4yHKtWrUpMTIR6666urn379h06dGhwcJDFYn311Vfz5s0jCKKnp0cul9s6MoIgGo0GauVbW1uhDPjEiROhoaFAtGvHgMNhMpng9FJRUZGbm5ufn289pc6/mTU8RwRBoGETwzA6ne7l5YVhWG9vL4vFio6OptPpEFJwdnbmcDgmk6msrOzMmTMdHR1W+lIoinp5eaWmphIEIRaLd+zYAR1TyJ3VF0gKe3p6amtrx2wDs3wMCIKQSCRPT88pU6ZgGKbRaG7fvv3xxx9LpdLBwUEURUUi0bp165YsWQL959OnTz916pQd/h+JROJwOGq1Go4vVCo1LCxs0qRJCIK0t7fbJy5hMplKSko0Gk1xcbGFyhVGfuGFFxgMxvfff9/X12frsBiGzZs3D/osGxsbH3zwwdraWsuuNXXqVOjl+f777wcHB20dHEGQoaGhwsLCsLAwC1Xn5MmTKRRKf3+/fQMOB4vFAjqa5ubmyspKmx7sSLMGSYfo6GgvL69Zs2ZFR0eDSIVCoZDJZGw2u76+nsVixcbGguPb0tJy9OjR6upq63deDMMSExP9/f1VKhVQfMOXTdyhvgUim8rKSgaDYX3xOPAlUKnU1tZWKpVaVFS0Z8+e9vZ2aFAFQggejwdhOGgRh6/X1pUVw7Curq6SkpLs7Gyj0chmsyMjIzUaTWZm5qVLl+xoKiMIoq+v7/r167B3a7VaMpksEok2bNiQlpZGo9GuXLlSUFBgx1KN4zh0sBuNxnPnzoFNEwRBo9FOnDghEAggAPXll1/azYasVCpdXV09PT27urq4XO7ixYtJJFJjY+PdUk82AUXRjIyMNWvWtLS05OTkuLm5GQwG69Wb/s2swaTCwsJeeeWVyMhIFosFjUYYhoEHqdPp3NzcnJ2dhUIhrAH19fWg2WN9Ax+FQnF2dtZqtVlZWZmZmfecKEEQMpkMqAsQKxg4LZ/E4OBgVVWVRqNpaGjg8/kgesTlckUi0ZQpU4BvzmQyQcun3e8SAghSqZTNZoeFhYWHh9fV1Z07d87ufiedTnf79u1Zs2YtX76cxWKFhYVNmTLF2dkZKCIgkmPfVLlcLoxfVFSE3EkdbNiwISoqCn7hs88+c2RlbWhokMlkUVFRdDp92bJlNBrNaDQeOHDAwVZAFov1xBNPIAgikUj6+vomT5785JNParXa2tran3/+ecxvZqRZm0ymoKAgDw8PHo9nOW+BoARwZXC5XMsuqdVqL1y4MDAwYL03CaFZiG7m5uaq1WpLQ7/FnaDT6enp6VFRUb29vQiCDCfiv9/DArvX6XQajQZEFMLDw+fPn+/m5gZiQkql0s/PTygUwin71KlTYrHYMpr13URwmoEty2QyeXt7p6en+/v7//zzz47otcFnLBKJ5s2b5+npCSQ1IJ1Dp9Nnz57d3Ny8bds2O2ylubk5NDRULpcnJCQ0NjZKJBIvL68XX3wR2qiUSuW+ffsc6aTSarXnzp179913hUJhamoqjuPd3d0FBQV2D4ggCIZhr776akxMjMFgEAqFzs7OHh4efD4/Pj5+1apVmzZtAkLkUUYYeWRUqVSwWYOdAdU+bNYajUYul3d2drLZbH9/fwzDysrKTp48CUuU9Y8GwuwUCsXDw2Pq1KnQK3r79m1owKRSqRkZGevWrWMymQiC0Gg0tVoN7iCdTr+faIjFKVer1b29vampqcHBwUFBQRbdPaPRCHcBJ6eTJ08OH8qmJjmz2dzW1gasYiKRKCIioqWlpbm52ZEwLXxsoDegVCr7+/uvXbsGZ7vHH3986dKl8+bN++yzz2w92BmNxjVr1mzevDksLIxEIgUHB3O53NjYWIFAAGvW7t277Q50WtDb26vRaNLT0yEvk5mZqVQqHUmiRUVF/f3vfwfRPRaLVVdX99tvvzGZzJiYmA0bNkydOvXrr79eu3btKLxqI80azrBAwa3RaIaGhqRSqUqlunXrllgsbmlpiYqKevPNN6lUqlQq3bdvn0XDzkrLgDBqdHQ0jUbz8fGZPXu2h4cHh8O5dOnSgQMHEARJT09/8MEHQXprcHAQPGA4yI8phIMgCNBvy2QyCF1ZZmXRIzQajR0dHc3NzRadJMSWMDOKomQyGTjmWCyWn59fX1/fuXPnLMHN4fRiNn3tBoOhpqZm//79KIreuHGjsrISiLd37969cOFCgUDAYrFsNWuCIBoaGrZv385isVQqlU6nI5FIcXFxECbSarV79uxxXGnOZDLt379/2bJlYNZZWVmOjEmn05955hkmk2kymTo7O59//nngm0YQpL6+/uzZs6dPn546deq2bdueeOKJ+z3ekWZtNBrr6+tffPHF2tpahUKB4ziZTB4YGAC5NyaTuXTpUi8vLwRBuru74cwEf2jl+8MwbPHixT4+Pk1NTfX19S0tLYsXL3Z3d1++fPnKlStBjlahUHR2dh45cqSsrAyIFqx8IpAthzUJ6L6BoBb02oDeCYhmLLQetjYzYxgGGoFkMtnNzY1Cofz88883b94crggKlg2HS+uXcIIgiouLQZcMBHnh33U6HYPBgLuwfp4WALOcZUUwm81LliyBYpv6+vrOzk47xrx75nV1dUVFRYsXL4a4uCOjoShaWFg4derUqqqq999/v7q62vIoYE87f/58WlpaWloaiDDdc5CRZk0QxKVLl8xms+WtD1/wgoKCnnzySRKJpNVqjxw5olAohgfmrAGGYa6urlQqVSKRXL58WSKRXLhwYcWKFatXr/b396dSqQMDA0AzLhaLZTIZhLFxHAcXefQECo1Gmz59ekhISENDQ3V1tcFgoNFoKpUqICAgNTWVwWDAO66srDQYDBaKI6hAsNJoKBRKcnLy7Nmz9Xo9iURqbm7u6uqCKJAlPEomk4EtxHpeC8iVQFx2+OEbRdFly5bhOO4gp70FZDI5ISEB3unrr78+XqKgOp2uoqJi/vz5jhMeDA0N/fjjjydPnoRj0t0Dnjp1atu2bSaTCRzUew4y0qwtBm0BjIthGJPJfPvtt+HIWF5enpmZaQehDNQGDQ0NNTc3K+9g//79jY2NjzzySHBwMCxOXl5eCQkJwLulUChcXFyAmn+UkYFULTg4GEheysrK2tvbqVSqwWBISEiYMmUKkHjA8m8xHVi3rCeY9PPzmzNnTmBg4ODgIIw/Z86cW7duQQyUSqUyGAxgFVOpVMCEPeawUDRGpVJNJtOIFykQCJYtW6bX648fP279RzIKZs+eDcElvV6flZXl+IAAs9nM4/FgAYqPj8/Pz7d7KIIg9Ho9LPn3tC6FQgFPXiAQ3O9gMLYaAaxAGIalp6fHxcUByd2HH35oX9mN2Wzu6uqi0+k+Pj7Ozs4Q65DL5VeuXJHJZOnp6cHBwYGBgaDWI5VKFQoFRK8pFAr88ghYNhMoiY6MjMQwrLu7G0IuCILQaDShUOjk5EShUAiCUKlUzc3NFq/XGp4ky4WoVGpCQoKPj49cLh8YGKBSqSEhITNnznzsscf6+vrKysp0Oh2LxQIi6srKSit3AAaD4ePjQyaTm5ubdTqd5XaEQuHhw4eDg4Nzc3O//vprxxdCFEV37doFPx84cGAcK9rBJYNda8qUKXA6d2TAUW6WzWYzmUw4Ad7vd6xKnuM4Hh4e/tprr7HZbKPRePPmzbu5aK10Us1mM6SXg4KC4uLijEYjmCCDwejr68vJyQGhEHd395CQkN7eXkjmgebkPQe0GAGNRhOJREC37OXl5efnB/LsPj4+S5YscXJyAoWXzs5OKO+0zNb6cLuHh0d8fLxGo+nt7e3u7lYqlUajcerUqaGhod7e3t7e3gaDobOzs6enRyKRWJmXAWmERYsW5ebmNjc3gyeD43hERERmZqaTk1NdXd1zzz03Lks1l8v19vZG7hCaOT6gBQKBAMfx/v7+/v5+kKK1T3JkOCxe4vB/xDBs2bJlWq326tWro+zeVjGmOjk5vfbaa+Hh4SQSqbe39/DhwzYV6w0HQRCFhYWnT59OTU1ds2ZNRkZGQ0MDhmFqtbqmpmZgYEChUIBI0tDQEGzo8HVac0U/Pz8wbgzDgCJfr9fDboUgSH9//6lTp3bu3NnS0jL8FGLNtMFPCA4OBiWAgYGBmpqatra2tra206dPBwQEODk5RUVFYRgmFovFYnFPTw9wl405PplMDgkJmT9/vru7u0Qi6enpEQqFTz311MaNG2k0Wm1t7dKlS0GO2pp5jn4LL730EjhdEAZ1cMDhgHpUuVwOtyAQCLq6uhyfMxxRLB4jiqIJCQmbN28eGBj4/vvvR9ltxjZrDMOioqISEhLIZLLBYLh8+fKVK1cc2WIUCsWuXbsIgoBK+aCgIGdnZ7lcfuPGjcuXL5vN5qKiouLiYhRFCwoKWltb+/r6QILjnqNZTMdsNsMiChFD8BkgqiCVSouKig4cOFBQUOBIcrGqqqqkpIRKpebn50NBCPAy1tTUgN0DLzrkrayPtPj5+fn7+0MZNLRWQBFYSUnJ8uXLQSTEjgmPAJlMXr9+Pcynra1tXMa0APJ0AoGAQqGo1WpXV9fe3l7HmyooFApkuAmCADHyF154QalU/vbbbxUVFaO8R6tWa5lMJhaLaTRaQUHBP//5z3tGT21KZ3R3d3/88ce///57QkICgiACgaCgoODWrVtKpVKn08HZDkXRoaGh4QHEe17CEng2GAzXrl0LDg4Gnn0ajQZKanV1dZmZmVC1YlMgecRVhoaG2tradu3aBVGLu4cCalb42fo6FgzDKioq+vr63N3dw8LC4Pl0dHR8++23u3fvHi+uTQRBSCSSq6sr/KzVase3uVitVqvVaoFA4O3tHRAQYDAY/v73vzto1giCsNls2CERBAHBwVu3bl28eLGoqGj0J2OVWZPJ5IKCgqysrJycnMbGRscZdU0mU19fX3Z2dnZ2tiPjjBhTKpX+61//unr1KkhhQK7YaDSO8lnbFLeGUgIrf9PKX4MChMHBwXnz5qEoWl1dffHiRYlE4vhDHgF3d3eLKYPIyzgObjQav/766x9++AH+74ULFxwfn7hDhRwZGQmKunq9/uLFi52dneNACw/bK51OHy9Vsj8asAT+R0z1fxN0Oh1yAlqtNikpadyfD0jeTJ8+PTo6ehwHx3FcKBQKBAIGg8Fms8exD3oC/z0Ab/XPnsUEJjCBCUxgAhOYwAQmMIEJTGB8McFXZj0mYiV/PiB2DtUgGIZBxzWLxaqoqIDWV8i36fX6pqamu0ss7bicj4/P3Llzi4uLy8rKxjc6/hfBX86shxe4gOi8m5ubVqvt6+sb3wzCHwqwUSsnDOSX0Avj4+Pj5eU1e/bskJCQ8PDwgYEByNc0NDRcu3ZtaGjIUuJn98Rmz559+vRpMpnc2tqalJRkkxr0fwqsquAb3siE3HlnFh1I+xSR73chy9IF/0KhUB577DGhUPjyyy/bJA88fEwSicRms0NCQkgkkkqlampqAhlFxyc84kJQfOfh4bFw4cKwsLAbN24cO3ZslIocuFlIkQBlR3t7OzDHrlmzBhqKS0tLb9++XVFRAQXcDs5QJBJ99dVXNBoNQRDge7G1P+hPB0gHjp6FHc2s4SXx+Xw+n+/s7AwFh66uriEhIR4eHmw2G8dxsVi8f/9+4KFzcLpkMpnP50PLHUEQOI4LBIJHHnlk2bJlZrM5Li7u6tWrto5JpVInT5782GOPxcXFQbuuTqerqqr67LPPbGLBvB8sHTHgPEBze1JSUkhICIfDkclk7u7ubW1t1gwFkzEYDIODg05OTsHBwZ6enha+PyiPgeIqu2dLp9PfffddHx8fWI/q6+vHMTUD9LmPPPJISEiI0Wi8fv36r7/+2tjY6Lj+Ktghh8MJCgp66aWXUlNTTSbT1q1bf/zxx/ux09zbrOFVUSiUxMTE1atXx8fHA1uIwWAQCAQcDofH4wFPSFxcXGtrq91sRhYwGIz4+HgfH5/s7GygZyAIAuhUoI7Zjpp36NT48ssvXVxc6uvru7u7hUKhr69vZGRkampqZWWl3WYNmxWZTGYymQKBAPhqly5dGhUVxefzyWSyXq9vbGwEggdrBhxe/E0QhJubG/D1MJlMGo0WFhY2b948vV5fW1sLJT52eNgYhoWEhMybNw9BEIPBcPv27W3btvX09IxLySuDwXj55ZefeuopLpcLzUdJSUkIghw6dEgmk9nBHjh82r6+vq+99lpycrKTkxOVSiWTyWq1WigUjvKF33e1hoKvp59+etasWVQqFVovgQQHGNqhIZzNZoOGu32TRu50AKxZs+bpp5+uq6u7ePEi1MeZzWYSiSQUCqEg1tZLoCjq5eW1bds2Nze327dv79q169atW+7u7m+++eb06dMDAwNJJJKtHJDgz/B4PD6f7+PjAzS1AQEBQ0NDAwMD0EULPXZarfbSpUuHDh0avV/1njcF3gh0Rkul0tu3b585c6a+vp7JZIaFhbW2tkINkE2y3NBrs2vXLjabDQ1KO3fuvHHjhuPdCTDyTz/9lJiYCG9KoVAMDQ2RyeS1a9cWFBTYvcPAQTkjI+O9994TiUR6vb6jo4PP57NYLJlMdu7cOZsLU8G79fT0DAgIAP5IrVYrkUiggTk4OJhMJsOertfre3t7HVn2OBzOm2++uXnzZhKJJBaLLV82juNz5sxxd3fHMKynp6eiosKmYXk83ttvvx0WFtbd3f3pp5+WlZWpVCqVSlVeXj5jxozJkyfbuv+iKMpisdavX5+amurs7Mzj8eDJ6HS67u5usVjc2toaHR0dHx8/ODh44sSJs2fP9vT02PpGQZ5h06ZNKIoWFRXl5uaKxeL6+nqz2ezp6RkcHAx9ANAabP2wJBJp+fLlwO4CVKDXr18f3i1vH+D1HTx4MDExUSqVfvvtt0VFRc3Nza6urm+88UZQUNC0adMqKyvt+HhQFBUIBJs2bXrppZd4PF5PT8/HH39cUlKyYsWKefPmXb58uampyR7f2mQytbe3t7e3BwYGGgyGtra2oqKi1tbWyZMnR0ZGQpun0Wisq6vLy8uzb5fBcdzV1XXbtm2rVq2i0+m9vb2ZmZmWYm4fH5+///3vQDR85swZmx4NmUxeuXLlnDlzDAbD/v37i4uLLeW5HA6HRqMB0YL1A0JTQkxMzNq1a6Gv7NKlS/39/VKptKKioqOjg8ViOTs7R0VFdXd3l5WVHTlyxHquzeHgcDiLFi0C7gez2dzc3NzS0qLX65lMpq+vr5+f3/LlyxsaGqBm3XoSC5FItGzZMugS6urqsjDUOHJeRFGUz+e///77sbGx169ff+aZZzo6OsxmM7QIuri49PX15ebm2kGLjKJoTEzM9u3bExMTDQbDxYsXt2zZ0tPTw2azqVSqQqE4duyYnfXWZrNZKpX+85//JAhCqVTeunWrq6vL19c3IiICHGuTydTT07Nnz562tjb7WA9jY2N37twZHx8PZDq7du3KysoCU6DRaC+99JK7uzuCIO3t7YcPH7Z+Q4APfdWqVUwmE1ZNi99PoVASEhJwHG9tbbXJ5mDMGTNm+Pr6Go3GU6dOffHFFwMDAwaDAYjQPTw8MjIyoqOjr169evDgQftsGjjWgCsQw7D8/Hw+n+/q6qrX693c3FxcXCQSiUQicXV1FQgE1psjhUJZt27d5MmTyWSyRqO5fv06RBKHhoZ6e3sVCoV9lk2lUpcvX75q1SqpVPryyy+3t7eDTXt7ez/wwAM9PT179+4tLy+31YFEUdTb2/urr74KDw+XyWRvvfXWuXPn5HI5iqJsNjs0NJTFYkGT9SiD3Nesoa+9sLDwqaee4vP5wKE4depUb29vOBPI5fLjx4+fO3fO1sMciqJcLvell1569tlnmUwmhmFDQ0M3b948fPgw8J5hGObj4xMXF4cgiIUzyaZLuLm5eXh4KJXKEydOSCQSOIxjGBYTEwOstT///LNNvilEJBISEhQKxblz57777jtovDebzdBmMWnSpClTpnR1dR06dMjCe20TwEmdMWPGjBkzmEymVqudM2cOnU4vLi4GtpOenh6pVEqn05cvXz5v3rzffvvNygacgICAhx56iM/nm81mjUZDpVJfeuklFxcXNpvd2tr6zTffnDt3zg6HhCCI9PR0iPAGBwf39fWhKDp//vy0tDQymbxjx47CwkI7vm0KhfL6669HRUVpNJrPP//8xIkTsN4DcVJcXFxPT8+YXJijBfjAsiUSSX9/v7Ozc3x8fFhYGI1GA7KY+vr6n376yVa2NRzHk5OTv//+e5FIBNlgpVJZXl5+/PhxjUYDZ2onJ6ennnoqICAAQZC2trbffvsNCKqtvxCbzeZyuUCXalktWCzW448/TqFQKioqLly4YOtbxDCsv78/Ly/v9OnTAwMDwJ8GzsmqVauWLFnCYDDOnTvX1dVlPXnscPB4vJdeemnTpk1gfxQKhc1mA212YWGhVCrt6+uTSCRisZhMJru6ulp5CRzHU1NTvby8ID1kMBiWLFkCuzmO4z4+PgkJCQUFBY8++iiQJls/YYPBcOrUKRDZ2L9//8DAAPSJ5ufnf/311yUlJXbYNJzoli5dimFYTk7Ot99+a7FpLy+vZ599Ftjyx5zn2DwhxB3SVBKJpFarTSaTpY2qv7/fpgeBYdjjjz/+0UcfQQsqgiBarTY7O/vy5cuNjY1sNtvZ2Xnq1KkPPvjglClTaDSaUqnk8XiBgYFlZWU28SWDQfP5/OTkZGgoJpPJixcvnjNnTl9fH7R52jRzEBK5dOmSQqFobm4mk8nALcHlcletWrV+/Xo+n9/T01NXV2cHFzBsr3v37l28eLGF+BiCIQaDQS6Xy+VysVgM2gwEQfB4vKGhISu/cy6X+/DDD9PpdARBSCSSi4uL5aLEHebvxMTEd9999/HHH7dp4zWbzadOneJwOO+//z6EfQmCqKysPHHihH02jSAIjuNr166l0WgSieSVV16B8CjY9PPPP+/r60smk8dHZANieWQyWaFQlJaWQgcOgiCwCtq0iMbHx7/zzjsQQEAQBIK7CIJMnTo1JiZGqVRCvMzZ2RlCv0DJBy8DImjWXIUgiMHBwf7+fl9f340bN96+ffvKlSvR0dFbt25FUfTgwYO3b9+29TBAEERvb29JSQlEHoEXEzRoIiMjORwOBJWB8sb6BwIxLG9v7y+++GLWrFlkMhmupVAoLl261NfX197eXldX19nZCYzlrq6ukyZNEgqF7e3t1jx5DMPWrl07efJk9I7IBMR/jEYjENVCmJlGo3l7e9vRTGU0Gr/77ruDBw8mJCR8/vnnwcHBTCZTqVTaHRnDcdzLy0ur1d6+fdsSTY6MjHzmmWfi4uLIZLLJZJLJZGOOP0aWERxHFxcXFxcXoKqRSCRMJhOyl+7u7lKp1OKkWp7y/Z74li1bgGeDIAiVStXX1+fk5JSenq7X6xUKBXjw6B0Af1dHR0dPT4+tp9KWlpY9e/a88MILQqHwww8/lMvlrq6uLBarvLx837599rEZQfM5h8Px8fEJCAjYvHlzSEgIkKKDwtA9G/JHNz4qlTp//vyXX345KioK0lsmk6mqqurRRx+Vy+VkMlmr1arVagjqcbncWbNmrVu3DkGQixcvWvPxkEikFStWDFdtNZvNJpOpra2tpaWFw+GAk2M2m48cOWJ3yY1Op8vLy8vIyLhy5YqXl9fixYuLi4vtGwrDML1eD+oAr7zySl1dXVpaWmRkpFAoNJlMBoOBSqVaMruj4L5mDZt4amoqKIjR6XRo566qqhIIBM7OztHR0W+99dbbb7/d0NBgUU0G3POJoygaFRUFEzIYDM3NzQqFAjxsEonk7OxMo9FIJBI8XDiIKJXK4uLi4uJiOJlZvwrq9fpvv/22tbX1k08+8ff39/T01Gq1FRUV69evt08GCXxokUjk6ekZGBi4du1aWN4g9dDf3+/p6ZmYmJiYmPj777+Di2nNhNPS0j744AMnJydg99LpdPn5+Z9++mlNTY3BYIDiByD2dnZ2Tk1NnTp1qru7e2lpqZVMpxQKhcvlwjO3PNKmpqZr167FxcWBTjFBEEVFRadOnXKwlECj0ajVahqNtmHDhu3bt9vH6gRsyEuWLAkKCvL394fHbjAYWltbS0tLFy5cSKPRdDrdmK7IfZPnFApl8eLFb731FovF6uvr6+np6e/vb29vd3NzEwgENBqNSqXGx8cvWbJkz549Vt5DdXU16DhKpdLKysq+vr7Ozk69Xk+j0SIiIsDEIU+u1+sbGhr2799/4cIFmUxmq3YWciemDjrksAbs2bMHznM2jYPcSTpMmzYtOTk5ICDAy8uLw+EA53dlZaVCoZgxY0ZYWBhkUi5fvjzcNxtl2iiKPvbYY35+fnq9Hqgo8/LyLl26BFl9ONUIhUIqlTpt2rRFixZBLYdcLm9sbAR3aMyZD58D+Da3bt2Sy+XLly8HNWuCIKRS6d///nfrfbz73QuCIKWlpTExMQwGA0Qr7RjHZDIdPXqUz+dnZGTQ6XSoPiguLj558mRAQMDSpUsNBkNVVdWYq8Z9s4wQZYPKBBaLZTAYgAgPyhWAyx7H8cHBQSuFYwiCePTRR5999tnU1NTLly/DFyKXy2tqary8vIKDg4H6EbKvRUVFH330kVgs1uv19uV6qFTq+vXruVyuUqmkUCiQYkRsJ7RGUZROp0+ZMiU9Pd3Z2ZlEIlVXV+fl5d26dSs/P99sNoeEhMyZM0er1SoUCjgyIlbXM8I6TaFQhoaG+vr6AgMDhULhvHnz8vLyqqqqZsyYsXbtWigfAG8Y9K2PHz9u5QEaxCQsd93f39/T05OamgpFVAiCKBSK999/v7Gx0fEabqPRmJ+f/+CDD6pUKrsJ+KAu4LPPPtu7dy/4uvBgURRNT0+n0Wgg4GZ/JESn0xUWFm7cuBGKE4qLi7u6utLS0iCbjSCIVqs9ceLEkSNHrNe2UqlUe/bsOXDggEajoVAonp6eSUlJbm5uc+fODQgIsCiXXr58+fPPPwdRXfseN51O37Jly8qVK0FfmUqlkkgkLy8vCoVik2MNdyoQCKZPnx4TEyOVSi9cuFBSUtLV1aXVakHmKzk5WSgUyuXy77//Pisry6aCNVgvQRGPwWBQKBQ41S1btgyuDiERjUYzMDBw/vz5n376qb29XSqVWn8XFi48FEU9PDyWLl0KuQKz2TwwMLBnz56DBw86SJ1qOYmCY2mRbrMPEFbu7+8fGBiAkjII/qxduxY2q4aGhjFXutGS56WlpVeuXJk7dy5Q8EOKBKSSdDpdVlbWzp07LSIbVs4YwlUIgpDJZC8vL29v79mzZ/v4+IBOQE9PzxtvvHH+/HkQPxhzH78nUBRNSEhYt24djUa7evWqRqPx9vaG6CGTyRwhGzD64LDZwTHR19dXKpXK5XKTycRkMiEusWHDhkWLFuE4npWVdfr0aZvU61AU3b1794svvhgQEEChUJhMpuW4bBkEtBOOHTuWmZkJe9c9edJGmf+JEycWL14MDRlMJhMcJLPZLJPJXnvttRMnTtidZUTu6LsKhUKZTAYakBYySPsGtMDy6sFxCAkJcXJyMplMDQ0NkM4c/c9HyzL29fUdPnx42rRpLi4u8+bNo9FoTCYTUozV1dWffvppe3u7recMy8pBEIRWq+XxeFwul0qlGo1GsVj8yiuvXL16FUKHxLBmAptAJpM3btzIZrPFYnFHR4ebmxuGYa2trSUlJXcXlljjk/T19fX19cnlcpFIlJCQ4OXlpVarfXx8QkND4+Li1Gr1lStXdu7caWu4hiCIkydPXrlyJSwsbMWKFUlJSXBuJggCyP0vXryYlZUFBa62qj4AwA46Ojp8fX0tum0KheLkyZOfffYZyDjZbdNAYj9//nyNRlNRUQF6RTweTywWj0uLhsVUqFQqCLYbDIbs7Gxw80bHaAE+k8lUVFR07dq15cuXczgckDyDIpsdO3aAZo99DwWeb09Pz9WrV+GJl5WVvfvuu2KxeHgJgX2Du7m5xcTEYBhGo9ECAwMZDIZCobh582ZZWdnd6sLWXEKtVkN5hre39/Tp0xEEgY4KFEW7urq+++678+fP21HGSBAE6Eh0d3dfvnwZGdYcZP16POYlysrKpk6dCvUqEImrrKyUSqX2pUItgJz8e++95+/vr1Qq1Wp1VFSUQCBQKpW//PLLeLXngRMiEokWLlzIZrNlMllhYaE1g4+RjlGr1UeOHAkLC4uIiAA/oaOjY9euXb/99puDfQMEQSiVykuXLtXW1tJotIqKCkhhOv46DQZDe3u7s7MzCB5IJJKjR4/m5ORYikOG/zJ6L27wEfMcGhrKzs7u6uqC5+Di4gJrXk9Pz8mTJx1sABn+h+NiyiMA/sbhw4ePHDkyjuMTBNHV1dXa2gr0+1Cl3NPT8/DDD9sdtL7nVSgUyvTp00UiEUEQjY2NdXV11tzFGLs8FB/Onz9/1qxZKIo2NjZmZWVBBmicZm5zaGJMkMnkxMTExYsXx8TE3Lx585dffmlqatJqtSPWpxEyp2MC8sxUKhWEpdVqtcFg+A/qGh534DgeExPz1FNPzZ49m8Vi9fb2vv7667/++uv4NomSSKSYmJgPP/yQQqHs3bv36NGj1iTP/3Kd5xP4zwL4CVD49cd95GNuqhOYwAQmMIEJTGACE5jABCYwgQlMYAIWQCTBy8sLWkAmMIH/eJBIpOjo6HfeeefChQsZGRnQg/PfDauoJS1A/51aEiizJqKJf3Hw+fz169dv2rQJw7D4+HiouvmzJ2UboAHA3d19xowZfX19BQUFo/fRWmvWkGPj8Xienp4ikSgkJGRgYKCgoABY4f6Lk22jJEGB7xB4N+l0OghRww9arba4uBi4y/6XJ3w3AgMDV65cSaPR6uvrT5w4YROTxF8BKIoymcy0tLSHHnooKipqcHBwx44dWVlZo1R1W2XWGIZ5eHjMnj3b19eXx+MxmUyoQ/fy8tq9e7fjou3jDngQLBZLpVIxGIyAgICNGzeazeb333/f1pqk+zWw0Wi06Ojohx56KDAwkM/nQwMO1FeZzeaGhoZffvklNzd3dA4+KwFpPKidtLXmDkXROXPm8Pl8mUz23HPPAe+Zg/MZUVk5IgU4vrs3hmFMJjM9Pf2JJ54ICQnBMKyurm5MFjirOs85HM78+fOXLVs2MDBQVFRUV1fn6+s7c+ZMT09PDofT09Nj/SzRO4T7MTEx0E9eV1cHHYGOFEmOuERISMjzzz9fWVl56tQpMpnM4XAkEsm8efOWL1++f/9++3iyh48vEAgeeuihzZs3c7lc4JmQSqUDAwP9/f1BQUGBgYH+/v4UCqWysvKeZk0ikYxG45jFMPCsaDRaQEBASEhIc3MzdLbbOlug3cjMzCwoKHDQpnEcnz17dkZGhlwuZzAYZrM5MjLS29ubz+eDvDxBEM7OzgaDoaKi4p133rl9+7aD+xWJRIqIiEhKSlIoFN3d3TiONzY2jkkwNLZZk0ik2NjYmTNn9vf3/+tf/6qvr2ez2TqdLj4+nslkQumW9UBR1MvL64EHHti4cSN0BA4NDQHB5rVr1/bt29fd3e3gLgnt1iEhIV9//XVPT4/ZbG5ra8vPz/fw8Ni0aVNZWVl+fr7d3w/Y9JYtW9auXctgMKRS6a1btzIzM2/duqXT6YxGY1BQ0IcffhgYGMhisYD0424A68D9LAysGXgOGAxGamrqc889x+Vyf/755+rqalsnzOVyQ0JCUBQtLy930MIoFEpMTMyPP/7I4/GMRqNGo4H2ahzH9Xo9n8+H34HqZTc3t5SUlB07dnz66ad2v1CgPouOjhYKhS4uLtA8dfXq1TFbH8YwayjijouLw3EcKNXMZjOLxYqKimIwGD09PcAmaP1EodkhMDBQIBCQyWRoiwTuhJiYmPXr13/55Ze7d+92hKA2IyNjy5YtJSUlFRUVlup7tVqdmZkZHx8fFBSUn59v38iwcT3//PMPP/wwiqIlJSXvvfdefX09bDVmsxmqAouKilgsVnt7e19f3z0Hge1ixGpt8TSge9LV1RWe0owZMzw8PFQqFXBX2PpBzp8/H3icgZLFETg7Oy9cuBAWMoPB0NfX193drdFouru7a2trtVotjuMsFovFYvn7+6enp3O53KeeeurgwYOtra12XA6eg7u7O1AgiUQiBEF+/fXX/Pz8MZVGxl6tGQyGQCAQi8Xt7e0GgwHH8cjIyOTkZCaTeeTIETtIjFQq1bVr17hcLnQ0UigUgUDg5+cHnTIrVqy4dOmSHQw1///9kEj/+te/2Gz2sWPHho9AEIRMJrO74wa5408/+eSTTzzxBIIg+/bt+/777zs7Oy0cV9DspFar29racnNzT506BbzJ95zk8G4JYIB3dXXl8/kkEkmv14eGhtJoNIVCAf3RCoXi2rVrx48ft3W5RVF0+fLlCIIAm6Z9N25Bd3f39evXo6OjQ0JCfvnll2PHjkmlUqDRgYlZAmU8Hu/MmTNTpkxBEMRutwc6yhISEoDNFMgIvvnmG2u4xMY2a7VaDWd8uVxOEATwZDo5OZ05c+b69eu2KvRAL9np06fPnTtHJpN5PB6IaSQlJc2ePXvy5MkikWjlypU1NTX2lXS7uroKhUK1Wv3zzz+PuC6TyeRyuQwGwz4PBMfxtLS0p59+mkwmHzp06Msvv4Q+zhENl0ajsaWlRaPRtLe33+8W4HAJEVLYAVJTU6Ojo3EcLywsVKlUHR0dg4ODIAQ1Z84cmUx29OhRO5oOyWRyYGAg8IDaxPZ2T5jN5mvXrgFfNZSbI/dqg0BRFAgszWZzf3+/3aX5KIoGBwfPnDkTeNrVavUXX3whFouteQhjc/ABpYFWqyWRSGQyOSIiIj4+vrm5+fTp04ODg3aYCIwJwlZKpZJEInV3d7e0tFRVVb3xxhthYWGzZ88+fPiwWCy2IygONEtA0Tv83zEM+9vf/ubs7Azt3LYOSyKRpk2b9sknn3C53IqKiq+++gpsGhoEwTqRO8Ru0H14PysEIgrLugtHopSUFDqdDgzicLowGAxkMjkjIyMsLOz69evAAWTTnBEEAbIvDMM0Gg0cUoc/EBqNBt34Go0GpPHGHFCr1Vqjy+Hp6SkQCIxG440bN+63ZY0J4O2PjIyUyWRNTU2XLl3Kz8+3cr8ae7U2mUyVlZWTJ08Gm3j00UfpdHpubm5vb6+DuRjoaCQIwmg0Go1GaHQPCgricDhJSUnQ0mJr/Xh/fz/owVEolOFBA6FQmJycDDSkUPNu/TxRFA0MDPz444/d3d3lcvmxY8d6e3uRO4QHCIJQKBQymQwEsBwOB8Owpqam0eMtFneITCa7u7szmczy8vLi4uLOzk6tVgvTg3gLgiA//PCDfWseOHjA9QoPBM4zbDb7xRdfXLVqFbA4oCja0dERFRVlTYxozOiNUChcs2YNk8k0mUzZ2dl2p34oFEpKSgooS+Xn5589e9b6E9fYZk0QRF1d3cyZM9esWaPT6ZKSkkA2wA49l3sCljqz2QysXyAZU19fDzS7ln0Nsc645XJ5S0sLm81evnz5sWPHYIlisVj/+te/gDyXxWLZOm3IBTg5OWk0mqKiohs3bgBjKuw5CIJQqVRQaDCZTCqVik6n9/f3j/J84HuD0zOcDoFdSCKRwH+CpBowkDQ3N5eXl9s0YQsmT54MTpdEImGz2UKhEOSg0tLSvLy8oIcNDqk+Pj6XL19OSUmxO2oBtIl8Pn/WrFkzZ87kcDgajQbIXuwbENYgMpk8ODhYUFBgk2tgVTpGIpFQKJSpU6dSqdTu7u633nqrtbV1XNppAbB0UalUIAwBzv0Rv2DlUFqtdvPmzT/88MPOnTvfeuutzs5OBoPh5eUlFApxHIfWaztoCfr6+nJycoAgtK2tzbJswMZtNBqlUimbzfbw8IiMjOzs7IS+XWsGN5vNOp2ur68PIkIsFgvOoN7e3lOnTu3t7X322WfvbpgHjOlNpaenA3EHkEWFh4fPmDHDy8sLQZDe3t7q6uqwsDDkjhhQVFRUfHy8fWEi8L64XG5kZKSvry9sESaTyRFBa2gz1Wq1YrF4ODeVNX9rlVmbzWYPDw9fX1+5XH748OHbt287qHt5TwQFBWVkZNBotJycnM7OTvt64wiCKCkpWbJkyZdffpmQkAAcVMD16u7u3t/fX11dbatZoygKbButra3AQgsLrYXMBESonJ2dg4ODU1NTKyoqbt68aVWDNIpCGMHf339wcBCo5sHrTU1NjYmJOXr0qIWW6e6/HdMfGBwcBA0QgUAASlyenp5UKlUsFq9bt669vR1qIjZs2PDee+/R6fSNGzfaHf2Eb5LP53M4HODZkUql1nB6jDKgWq3u7OxsaWnh8XhOTk6Dg4NWRt6sckJwHIftQK/XA1+j3XO9H+DYKxKJjEbj+fPnVSqV3YEhyF0vWrTIzc0tOjpaLBZrNBoWi5Wfnz80NHRPut7RJ0YQREdHh8FgAMoH+PfhizF8gTqdzs/PLzw8vK6uzvpEJkT0BgcHWSyWu7s7mUwmk8nOzs4ikchkMgFD0Ahh7BGxl/uBIIgLFy4sWLBg2rRplvxOS0tLS0vL119/DeFaBEEMBsPXX3+dlJT0wAMPKJVKR4gAgEzQoggMipJtbW12ODZQTtfU1ASKajExMRDS+f33363hvLVqtSaTyRQKRafTSSQSBzPP950HiQR6X9XV1UCJ6aCHYzKZOjs7LYS5bDYb3uLoClF3A0VRNptNoVCGUzIMDylY/gVF0SlTplAolKqqKiulWIABp6CgoKenZ2hoCGJNEJWbNm2aQCB44IEHnJycsrKyOjo6hoaGTHeAWOeYVVZWvvvuu2fOnOHz+X5+fidPnszNza2pqWlpaRnOJ0EQRE1NTXp6uq054+FPCTYHsVgMhBNA8WG9GMjdgLoxMpksFArpdLq3t7dQKExMTNy6datUKh192LG1CVEUhdo9BEEoFEpoaCh4TvbN9X6IjIycOXMmiqJFRUUjDgeWgIMjoFAoVCrVIoRgPXAc9/T09Pf3txCGj7BpmCqO45MnTw4PDx8YGAB26tGHHT7O4OBgWVlZa2trY2NjV1cX5CYNBoNMJtPpdB4eHpMnTw4MDHRycuJyuUA/OWIa94PZbL5+/fo777yj0+lCQ0OXLl3a2NjY2NgYHBycnJzs7u4OIjspKSkRERFAAW7r87E8B5C1HhwchBUElOJKSkocSccwGAx3d3dQYjl58qTRaExMTHz00UfHfI9WrdYgjARqKWFhYampqdnZ2bbKr4wCDMM+/PBDOp2u0Wh+++234XsWnK8toQO7LwH2R6VSgffb+j+kUqkRERGBgYGg9Xb3S4IZxsbGfvTRR3Q6vb293UpOdeROiBMiehqNBgR6RCKRh4dHY2NjZ2dnQ0ODQqGorq6GwPNwXkkrn4Zer9+9e3dgYOCKFSsmT5787LPP4jgeGhpKEIRSqTQYDFKplEaj8Xg8iUSSk5Njx0O2fO1UKjU9PX39+vUikUir1f7+++8dHR12vzUgoTYYDFlZWVCPkJCQEBwcvHDhwjHT21aZNdRUQHkxqCjQaLTMzExHPODhiIqKSkxMxDDMQhpt+U/gFDpOrWIwGCyP3qY/5PF40dHRXl5ecXFxUqnU8jHDYRHKJlNSUrZv3y4SiUCMENKxow9rcV0gOYUMY5nS6/Xt7e1lZWXACa/VaiF+D1EFo9Foa9xdr9c/88wzX3311datW+l0ukgk4nK5GIZB8ZCLiwtwSO/ataulpcX6YWHyFvobLpe7du3a//mf/+HxeCaTKTc3d8+ePY6wwUOeiMFgwIsDyRHLz6OfAawyawhggXIHn88XCARAh56bm3vPBczW2cPjhrPL8EpOeGS25ufvCajWgNyH9SqPULft4+OTmJjo5+cHZVImk0kgELi4uPB4PCqV6u/vn5iYCGUz27Ztu3r1qvU2RwzjzAWWaKPRqNfr29raoAVBoVAAXSrUjYA/ZkcFL0EQlZWVK1euhAtxudzg4GAOhxMdHU0QBJfLraqqKi0tRe4orlvzZGAycPaIjIx89tln58+fT6PR1Gr1iRMn3n33XYjh2P3ulEqlVCr18PBYv369j48PgiDJyckgWWY/EbAFBEHIZLJDhw6BoiuQ42MYNmXKFBASd2TqCIIkJCQkJiZCRmoEgxskIMfF1cEwTCqVuri4hIWFWSr7xgRBEN3d3U1NTVOmTAkNDQ0JCXn66afRO6pZIAEBUe3Dhw//+OOPYI5jThiswfJrYLWQHGWxWKBaBHUXEP6DeCKCIKDE5+AzMZlM/f39BQUFCIJkZ2cjCAIpUviQrIxLMplM0Gag0Wjz58/fsGGDr68vEDofPXr0xRdftKMGbgSkUum1a9e8vb0TEhKmT58OH7ZGo/nll196e3vHCG5aeQ0cx0Ui0dy5c0NDQ93c3BQKxenTp/Py8iyzt+8eyGTy8ePHQexr/vz5xcXFI8ZxJN404kJHjhyZOXNmaWnp2rVr+/r6rBwWRVFPT881a9akpqYKhUIGg8FgMGBl7e3tzc3NzczMrK2tBTp3m6Zq2cQRBCGRSE5OTp6enlA70NbWVldXB/Vx4E9jGAaa3DqdzhGFOLsx/ITKZDIjIyMXLVoUHR3t7u4uEolYLBaO4729vc8999xvv/02Lr2S6J3+xTlz5gQHB/N4vKamppycnIqKijH7DO2v0nTc2lAU9fb2/vXXX729vTs7O2fNmgW1FuN+IRjn8ccf37hxY2Vl5bZt2zo6Omz9cyD0hz0ajnrj0p4MKzeHw0lJSYmPj1coFPn5+c3NzSqVCgTVLUkfIMM1GAxQFjde53XrwWQyDQaDyWRiMBivvPLKwoUL+Xw+hULBMGxwcDAnJ2fnzp0NDQ1/hcZW2zrPLRivZ8pkMltbW9ls9qFDh+5ZdE/YqGh6PxAEsXfv3m+//ZawSwKCuFOP5eA0RgAS5jQabe3atXPmzJFIJPDlWKRLLDeOoiik0FUq1R+R4rUGkLKAesDCwkIQuyCTyf39/S0tLcXFxX+FfmTAn0wETKVSV6xYIZfLr169ancF4386YNfSarVDQ0M4jqtUqvvZB5zU/wrL4QQmMIEJTGACE5jABCYwgQlMYAITmMAEJnBvOF6DOmI0YB4a32En8BfHX+Jl4zju7Ozs6enJYrGAvg1SD5bcMmQlgJ3ImgGhEAc4gZycnCIiIiQSSXd3d11dna3dMRP4T4SdWcZxBI7jgYGB8+bNCwoK0mg0v/76K1TMWEosgEUb2v6szzhCm8ng4CBQkaxYsSIwMHDHjh25ubnjlY2HT25EcsRSxvS/n9yegAV/vllzudz169dPmzatvLz81q1bfX19UD8O5fkIggD3nIUTzEro9XqdTmepn9RoNN7e3rGxsdeuXXMwx4uiKI1GW7RokY+PT2ZmZktLC0wMaq89PT0NBoNEIrGPG2gC44J7mzWO41QqlclkQhsfm83mcDgKhUKj0Tg5OSmVSgzDampq7tfobz2oVOojjzySkZFRU1Nz+PDh+vp6KOKBirbk5OT09PQLFy6cPXvWpqIwiwND3OHFGxoaYrFYHh4ettbg3w0QRV68ePHg4KDZbLbQynh5eaWlpUGDBfzan1W8MYF7mDWZTH7rrbeWL1/O4XBcXFzgvDXiyGU2mxUKxbp1637//Xe7rQTDsICAgJkzZ1ZUVHzyySfAlwXfCTRjL126dMqUKUChYnchBJg4n8+HQkccxx0sm3RxcXnrrbdcXFyOHj2qVquh/i44OHjp0qVkMvnKlSsSicTCzDSBPwX36LQFsqmQkBAvLy9g/bH0QViA4zifzz9z5swjjzxid7sulUpdunSpWq3+7LPPGhsbR/TqQZsxj8cDJ8S+S8BsKRQKn883mUwNDQ2Os4gvX77c19e3r6/v5MmTcrmcyWTOmTNn375969ato1AoOTk5arV6vLofJmAf7m2RbDZ7+PJsNpv1ev3Q0JBKpVIoFHCYIwiCTCZ/8sknkZGRdoTPUBQNDAxMTEwsLS29mwMJx/ENGzZwOBytVnvjxg07lmr0DtcjhmFsNtvPzw9FUevJlu43ZkRExMsvv4xh2LZt21paWoBxMyMjw9PTU6fT7du3DyrsJmz6z8VIJwRFUbPZ3NHRIRAIwAKGhoYuX76cn59fXFwMhD2ffPKJu7s7tPWz2exPPvlkyZIlti6oZDJ53rx5GIadP39+hA+Koqirq+uSJUtMJtOxY8fq6+vtuDHwraGdMygoKDQ0tLGxsby83BGDI5FIzzzzjFAo7O3traysBJZAFxeXadOm6fX6w4cPW99ONoE/FCPNGjqfjx8/DuIJnZ2dV65cOXTokEKhAK5EEonE4XDWrFkTGxsLUkARERFUKtVWs2YymQEBAW1tbd3d3RbfBvrMyWRyamoqh8MpLi7evn273a4wekd7ZdasWSQSCShe7RsKQKFQIiMjEQQ5fPiwRVEgJSWFzWbn5eXt2LFj4oz4F8E9joxKpXLXrl2//PKLt7d3U1OTXC4fTmhkMBh++umnCxcuHDt2DOjmmUymrVeFBkEGg1FQUECn0y3xFuClBU0CUKa6HwOdNZcA0lsvL6+QkBCdTtfe3m40GiFwYem/tGlwg8EgFovlcvmBAwdgN3B3d3/llVdQFH3nnXcGBwftmOcE/gjcw6yBDqu1tbWtre3u9luCIHQ63cDAAJPJBP8VZI1suir0g9DpdKFQ6OzsHBIS4u/vz2Kx5HI5MI0LhcKzZ882NjY6sr7iOM7j8eLj48PDw3t6esRicUJCAplMBlUXFosFzjH4XdYMaDKZ3nzzTaPRqFAo4LP56quvGAxGTk5OVVXV8AYtZLx13CZgE+6bjhllJSMIgs1mBwUFIQhiNpt/+OEHW40PwzCBQEDc4fFHUVSr1crlcplMNmnSpBUrVqAoWl5e7uCebjKZOBzOjBkzXFxc1Go1m8329PRks9m+vr7t7e0gtwUt6FZKDZnN5r6+PstiHxISMmvWLIIg3nrrrRE8EI5MewKOw54sI4qiX3zxBdAjSaXSHTt22PoigctPJpPl5uY2NjbCoRDH8fDw8IyMDC8vr6amJru5ygHwzeA4npCQQKPRuru7c3Jyuru7gdoUugYtKXor5w8fAHj/rq6uR44coVAo165dq6+vnzDlvxTsMeuAgIAHHngAQRCCIDZu3GhH8RCKokqlks1mA7EdLHVMJnPRokWhoaEGg+GHH36QSCSO2Ark3t3c3LhcrlqtPnr0aHl5OZxrhw9ra2gSvhYymbxy5Upvb2+1Wr1582a7VX8m8AfB5kwKhmEFBQVQraFQKH7//Xc7rgoLHolEGs4a4+PjM2PGDLPZ/NVXXx0+fPietmKTFXK53MTERBqNJhaLL168CJ7GiE9lhENsDcCsFyxYgGHYtWvXHGFPnMAfBJtX67CwMIFAgCAIQRDLly+3+0g3NDTU2NgIjI8IgvD5/EcffdTJySknJ2ffvn33o7qy3oBgqV69ejWdTu/q6hqF7tEOVioURf39/Q0Gwz/+8Y+JJPlfEDav1hcuXLAEQHJycuy7qlarraqqwjBMJBJBgO+pp55asGCBRCJ5//33QRfUvpEBkCXZsGGDSCTS6/VZWVm2xmpGR0hICI/Hq6qqam5uHsdhJzBesG21plKpnp6eCIIQBPHuu+86ooPR29s7derU9PT0yMjIGTNmTJs2bWho6PPPP29oaBgXBrCoqKiVK1eazebm5uZTp06NY/IPRdEHH3xQo9Hk5eU5KM8+Wi08zgAAAS9JREFUgT8Itpn1k08+CT8YDIZvvvnG7quaTKbBwUF3d/elS5cyGAwOh9Pe3v7FF18A47zdw1oAlJ56vX5gYGDXrl3jmygB7vfW1taLFy9OeNV/Tdhg1iiKPvbYY1DEfOjQIUdEZAiC6OnpKS4uDgwMJJPJ5eXln3zyyY0bN8Zr8TObzdXV1QcPHqyqqjp37tz41mlAxaIlKTNh2f/ZoFAoUBai1Wohbe4IIPM8bdq0yZMnczicUQIR6B0i/r8IyGTyjz/+eOrUqdjYWDKZ/GdPZwKOYdmyZRAg0+l0ycnJ4zLm3Q0Kf33AeXThwoX+/v4TZv0fj927d4NZa7VaLy+v/zhzHF/8H7/9vzhs8K0rKiqUSiWZTJ4+fbo1ko//3fg/fvsTmMAEJjCBCTiM/w9S+KkuAnDBhwAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<IPython.core.display.Image object>"
            ]
          },
          "metadata": {},
          "execution_count": 26
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "show_image(generated_images, idx=12)\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 430
        },
        "id": "-r55SYbA1K1p",
        "outputId": "3c6946e2-5f25-4382-d8c5-511c0e1f0757"
      },
      "execution_count": 27,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "show_image(generated_images, idx=0)\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 430
        },
        "id": "4wM8xZcI1N9B",
        "outputId": "4738bc56-9cdb-4e19-e54c-f6c2b1946829"
      },
      "execution_count": 28,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "show_image(generated_images, idx=3)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 430
        },
        "id": "tw75tchc2tzm",
        "outputId": "b97b26f8-8cda-4233-f7e2-23c6beb6c133"
      },
      "execution_count": 29,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    }
  ]
}